The El Nio/La Nia and the Southern Oscillation(ENSO)is an interan- nual phenomenon involved in the tropical Pacific ocean-atmosphere interactions.In this article,the aim is to create an asymptotic solving method o...The El Nio/La Nia and the Southern Oscillation(ENSO)is an interan- nual phenomenon involved in the tropical Pacific ocean-atmosphere interactions.In this article,the aim is to create an asymptotic solving method of nonlinear equation for the ENSO models.And on the basis of a class of oscillator of ENSO models,using the method of homotopic mapping,the approximation of solution of corresponding problem is stud- ied.It is proved from the results that homotopic method can be used for analyzing the SST anomaly...展开更多
The El Nio/La Nia and the Southern Oscillation(ENSO)is an interan- nual phenomenon involved in the tropical Pacific ocean-atmosphere interactions.In this article,the aim is to create an asymptotic solving method of no...The El Nio/La Nia and the Southern Oscillation(ENSO)is an interan- nual phenomenon involved in the tropical Pacific ocean-atmosphere interactions.In this article,the aim is to create an asymptotic solving method of nonlinear equation for the ENSO models.And on the basis of a class of oscillator of ENSO models,using the method of homotopic mapping,the approximation of solution of corresponding problem is stud- ied.It is proved from the results that homotopic method can be used for analyzing the SST anomaly...展开更多
In this paper motion of rigid rod on a circular surface is studied analytically.A new analytical method called modified homotopy perturbation method(MHPM)is applied for solving this problem in different initial condit...In this paper motion of rigid rod on a circular surface is studied analytically.A new analytical method called modified homotopy perturbation method(MHPM)is applied for solving this problem in different initial conditions to show capability of this method.The goveming equation for motion of a nigid rod on the circular surface without slipping have been solved using MHPM.The efficacy of MHPM for handling nonlinear oscillation systems with various small and large oscillation amplitudes are presented in comparison with numerical benchmarks.Outcomes reveal that MHPM has an excellent agreement with numerical solution.The results show that by decreasing the oscillation amplitude,the velocity of rigid rod decreases and for A=w3 the velocity profile is maximum.展开更多
The present work describes the fractional view analysis of Newell-Whitehead-Segal equations,using an innovative technique.The work is carried with the help of the Caputo operator of fractional derivative.The analytica...The present work describes the fractional view analysis of Newell-Whitehead-Segal equations,using an innovative technique.The work is carried with the help of the Caputo operator of fractional derivative.The analytical solutions of some numerical examples are presented to confirm the reliability of the proposed method.The derived results are very consistent with the actual solutions to the problems.A graphical representation has been done for the solution of the problems at various fractional-order derivatives.Moreover,the solution in series form has the desired rate of convergence and provides the closed-form solutions.It is noted that the procedure can be modified in other directions for fractional order problems.展开更多
In this work,the main goal is to implement Homotopy perturbation transform method(HPTM)involving Katugampola fractional operator.As an example,a fractional order Hepatitis model is considered to analyze the solutions....In this work,the main goal is to implement Homotopy perturbation transform method(HPTM)involving Katugampola fractional operator.As an example,a fractional order Hepatitis model is considered to analyze the solutions.At first,the integer order model is converted to fractional order model in Caputo sense.Then,the new operator Katugampola fractional derivative is used to present the model.The new such kind of operator is illustrated in Caputo sense.HPTM is described to get the solution of the proposed model using the new kind of operator.Also,there are some analyses about the new kind of operator to prove the efficiency of the operator.展开更多
The current investigation examines the fractional forced Korteweg-de Vries(FF-KdV) equation,a critically significant evolution equation in various nonlinear branches of science. The equation in question and other asso...The current investigation examines the fractional forced Korteweg-de Vries(FF-KdV) equation,a critically significant evolution equation in various nonlinear branches of science. The equation in question and other associated equations are widely acknowledged for their broad applicability and potential for simulating a wide range of nonlinear phenomena in fluid physics, plasma physics, and various scientific domains. Consequently, the main goal of this study is to use the Yang homotopy perturbation method and the Yang transform decomposition method, along with the Caputo operator for analyzing the FF-KdV equation. The derived approximations are numerically examined and discussed. Our study will show that the two suggested methods are helpful, easy to use, and essential for looking at different nonlinear models that affect complex processes.展开更多
This paper presents a study of nonlinear waves in shallow water.The Korteweg-de Vries(KdV)equa-tion has a canonical version based on oceanography theory,the shallow water waves in the oceans,and the internal ion-acous...This paper presents a study of nonlinear waves in shallow water.The Korteweg-de Vries(KdV)equa-tion has a canonical version based on oceanography theory,the shallow water waves in the oceans,and the internal ion-acoustic waves in plasma.Indeed,the main goal of this investigation is to employ a semi-analytical method based on the homotopy perturbation transform method(HPTM)to obtain the numerical findings of nonlinear dispersive and fifth order KdV models for investigating the behaviour of magneto-acoustic waves in plasma via fuzziness.This approach is connected with the fuzzy generalized integral transform and HPTM.Besides that,two novel results for fuzzy generalized integral transforma-tion concerning fuzzy partial gH-derivatives are presented.Several illustrative examples are illustrated to show the effectiveness and supremacy of the proposed method.Furthermore,2D and 3D simulations de-pict the comparison analysis between two fractional derivative operators(Caputo and Atangana-Baleanu fractional derivative operators in the Caputo sense)under generalized gH-differentiability.The projected method(GHPTM)demonstrates a diverse spectrum of applications for dealing with nonlinear wave equa-tions in scientific domains.The current work,as a novel use of GHPTM,demonstrates some key differ-ences from existing similar methods.展开更多
In this study,by means of homotopy perturbation method(HPM) an approximate solution of the magnetohydrodynamic(MHD) boundary layer flow is obtained.The main feature of the HPM is that it deforms a difficult problem in...In this study,by means of homotopy perturbation method(HPM) an approximate solution of the magnetohydrodynamic(MHD) boundary layer flow is obtained.The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve.HPM produces analytical expressions for the solution to nonlinear differential equations.The obtained analytic solution is in the form of an infinite power series.In this work,the analytical solution obtained by using only two terms from HPM solution.Comparisons with the exact solution and the solution obtained by the Pade approximants and shooting method show the high accuracy,simplicity and efficiency of this method.展开更多
In this paper, the time-fractional coupled viscous Burgers' equation(CVBE)and Drinfeld-Sokolov-Wilson equation(DSWE) are solved by the Sawi transform coupled homotopy perturbation method(HPM). The approximate seri...In this paper, the time-fractional coupled viscous Burgers' equation(CVBE)and Drinfeld-Sokolov-Wilson equation(DSWE) are solved by the Sawi transform coupled homotopy perturbation method(HPM). The approximate series solutions to these two equations are obtained. Meanwhile, the absolute error between the approximate solution given in this paper and the exact solution given in the literature is analyzed. By comparison of the graphs of the function when the fractional order α takes different values, the properties of the equations are given as a conclusion.展开更多
The entropy analysis of viscoelastic fluid obeying the simplified Phan-ThienTanner(SPTT)model with variable thermophysical properties are obtained for laminar,steady state and fully developed Couette-Poiseuille flow.T...The entropy analysis of viscoelastic fluid obeying the simplified Phan-ThienTanner(SPTT)model with variable thermophysical properties are obtained for laminar,steady state and fully developed Couette-Poiseuille flow.The homotopy perturbation method(HPM)allows us to solve nonlinear momentum and energy differential equations.The Reynold’s model is used to describe the temperature dependency of thermophysical properties.Results indicate that the increase of the group parameter(Br=U)and the Brinkman number(Br)which show the power of viscous dissipation effect;increases the entropy generation while increasing fluid elasticity(εDe2)decreases the generated entropy.Increasing the Reynolds variational parameter(a)which control the level of temperature dependence of physical properties attenuate entropy generation when moving plate and applied pressure gradient have the opposite direction and decreases entropy generation when moving plate and applied pressure gradient have the same direction or both plates are at rest.Also,increasing elasticity reduces the difference between variable and constant thermophysical properties cases.These results may give guidelines for cost optimization in industrial processes.展开更多
The dynamics of a spacecraft propelled by a continuous radial thrust resembles that of a nonlinear oscillator.This is analyzed in this work with a novel method that combines the definition of a suitable homotopy with ...The dynamics of a spacecraft propelled by a continuous radial thrust resembles that of a nonlinear oscillator.This is analyzed in this work with a novel method that combines the definition of a suitable homotopy with a classical perturbation approach,in which the low thrust is assumed to be a perturbation of the nominal Keplerian motion.The homotopy perturbation method provides the analytical(approximate)solution of the dynamical equations in polar form to estimate the corresponding spacecraft propelled trajectory with a short computational time.The accuracy of the analytical results was tested in an orbital-targeting mission scenario.展开更多
In this study,we investigate the seventh-order nonlinear Caputo time-fractional KdV equation.The suggested model's solutions,which have a series form,are obtained using the hybrid ZZ-transform under the aforementi...In this study,we investigate the seventh-order nonlinear Caputo time-fractional KdV equation.The suggested model's solutions,which have a series form,are obtained using the hybrid ZZ-transform under the aforementioned fractional operator.The proposed approach combines the homotopy perturbation method(HPM)and the ZZ-transform.We consider two specific examples with suitable initial conditions and find the series solution to test their applicability.To demonstrate the utility of the presented technique,we explore its applications to the fractional Sawada–Kotera–Ito problem and the Lax equation.We observe the impact of a few fractional orders on the wave solution evolution for the problems under consideration.We provide the efficiency and reliability of the ZZHPM by calculating the absolute error between the series solution and the exact solution of both the Sawada–Kotera–Ito and Lax equations.The convergence and uniqueness of the solution are portrayed via fixed-point theory.展开更多
In this article comparative analysis of various semi-numerical schemes has beenmade for the case of squeezing flow of an incompressible viscous fluid between two largeparallel plates having no-slip at the boundaries.T...In this article comparative analysis of various semi-numerical schemes has beenmade for the case of squeezing flow of an incompressible viscous fluid between two largeparallel plates having no-slip at the boundaries.The medium of flow contains magnetohy-drodynamic(MHD)effect and having small pores.Modeled boundary value problem is solvedanalytically using Optimal homotopy asymptotic method(OHAM),homotopy perturbationmethod(HPM),differential transform method(DTM),Daftardar Jafari method(DIM)andAdomian decomposition method(ADM).For comparison purpose,residuals of these schemeshave been found and analyzed for accuracy.Analytical study indicates that DTM and DJM arequite good in tem of accuracy near the center of domain[—1,1]but the accuracy reducesconsiderably near the start and end of the given interval.HPM and OHAM residuals indicatethat OHAM surpasses HPM in terms of accuracy in the present case.展开更多
We have analyzed an incompressible Sisko fluid through an axisymmetric uniform tube with a sinusoidal wave propagating down its walls. The present analysis of non- Newtonian fluid is investigated under the considerati...We have analyzed an incompressible Sisko fluid through an axisymmetric uniform tube with a sinusoidal wave propagating down its walls. The present analysis of non- Newtonian fluid is investigated under the considerations of long wavelength and low Reynolds number approximation. The analytic solution is obtained using （i） the regular perturbation method （ii） the Homotopy analysis method （HAM）. The comparison of both the solutions is presented graphically. The results for the pressure rise, frictional force and pressure gradient have been calculated numerically and the results are studied for various values of the physical parameters of interest, such as α （angle of inclination）, b^＊ （Sisko fluid parameter）, Ф （amplitude ratio） and n （power law index）. Trapping phenomena is discussed at the end of the article.展开更多
The development of mathematical modeling of infectious diseases is a key research area in various elds including ecology and epidemiology.One aim of these models is to understand the dynamics of behavior in infectious...The development of mathematical modeling of infectious diseases is a key research area in various elds including ecology and epidemiology.One aim of these models is to understand the dynamics of behavior in infectious diseases.For the new strain of coronavirus(COVID-19),there is no vaccine to protect people and to prevent its spread so far.Instead,control strategies associated with health care,such as social distancing,quarantine,travel restrictions,can be adopted to control the pandemic of COVID-19.This article sheds light on the dynamical behaviors of nonlinear COVID-19 models based on two methods:the homotopy perturbation method(HPM)and the modied reduced differential transform method(MRDTM).We invoke a novel signal ow graph that is used to describe the COVID-19 model.Through our mathematical studies,it is revealed that social distancing between potentially infected individuals who are carrying the virus and healthy individuals can decrease or interrupt the spread of the virus.The numerical simulation results are in reasonable agreement with the study predictions.The free equilibrium and stability point for the COVID-19 model are investigated.Also,the existence of a uniformly stable solution is proved.展开更多
Analytical and numerical analyses have performed to study the problem of the flow of incompressible Newtonian fluid between two parallel plates approaching or receding from each other symmetrically.The Navier–Stokes ...Analytical and numerical analyses have performed to study the problem of the flow of incompressible Newtonian fluid between two parallel plates approaching or receding from each other symmetrically.The Navier–Stokes equations have been transformed into an ordinary differential equation using a similarity transformation.The powerful analytical methods called collocation method(CM),the homotopy perturbation method(HPM),and the homotopy analysis method(HAM)have been used to solve nonlinear differential equations.It has been attempted to show the capabilities and wide-range applications of the proposed methods in comparison with a type of numerical analysis as fourth-order Runge–Kutta numerical method in solving this problem.Also,velocity fields have been computed and shown graphically for various values of physical parameters.The objective of the present work is to investigate the effect of Reynolds number and suction or injection characteristic parameter on the velocity field.展开更多
基金Supported by the National Natural Science Foundation of China(40676016 and 10471039)+6 种基金 the State Key Program for Basics Research of China(2003CB415101-03 and2004CB418304) the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221) in part by E-Insitutesof Shanghai Municipal Education Commission(N.E03004) the Natural Science Foudation of Zhejiangnm,China(Y606268)
文摘The El Nio/La Nia and the Southern Oscillation(ENSO)is an interan- nual phenomenon involved in the tropical Pacific ocean-atmosphere interactions.In this article,the aim is to create an asymptotic solving method of nonlinear equation for the ENSO models.And on the basis of a class of oscillator of ENSO models,using the method of homotopic mapping,the approximation of solution of corresponding problem is stud- ied.It is proved from the results that homotopic method can be used for analyzing the SST anomaly...
基金Supported by the National Natural Science Foundation of China(40676016 and 10471039)the State Key Program for Basics Research of China(2003CB415101-03 and2004CB418304)+2 种基金the Key Project of the Chinese Academy of Sciences(KZCX3-SW-221)in part by E-Insitutesof Shanghai Municipal Education Commission(N.E03004)the Natural Science Foudation of Zhejiangnm,China(Y606268)
文摘The El Nio/La Nia and the Southern Oscillation(ENSO)is an interan- nual phenomenon involved in the tropical Pacific ocean-atmosphere interactions.In this article,the aim is to create an asymptotic solving method of nonlinear equation for the ENSO models.And on the basis of a class of oscillator of ENSO models,using the method of homotopic mapping,the approximation of solution of corresponding problem is stud- ied.It is proved from the results that homotopic method can be used for analyzing the SST anomaly...
文摘In this paper motion of rigid rod on a circular surface is studied analytically.A new analytical method called modified homotopy perturbation method(MHPM)is applied for solving this problem in different initial conditions to show capability of this method.The goveming equation for motion of a nigid rod on the circular surface without slipping have been solved using MHPM.The efficacy of MHPM for handling nonlinear oscillation systems with various small and large oscillation amplitudes are presented in comparison with numerical benchmarks.Outcomes reveal that MHPM has an excellent agreement with numerical solution.The results show that by decreasing the oscillation amplitude,the velocity of rigid rod decreases and for A=w3 the velocity profile is maximum.
文摘The present work describes the fractional view analysis of Newell-Whitehead-Segal equations,using an innovative technique.The work is carried with the help of the Caputo operator of fractional derivative.The analytical solutions of some numerical examples are presented to confirm the reliability of the proposed method.The derived results are very consistent with the actual solutions to the problems.A graphical representation has been done for the solution of the problems at various fractional-order derivatives.Moreover,the solution in series form has the desired rate of convergence and provides the closed-form solutions.It is noted that the procedure can be modified in other directions for fractional order problems.
文摘In this work,the main goal is to implement Homotopy perturbation transform method(HPTM)involving Katugampola fractional operator.As an example,a fractional order Hepatitis model is considered to analyze the solutions.At first,the integer order model is converted to fractional order model in Caputo sense.Then,the new operator Katugampola fractional derivative is used to present the model.The new such kind of operator is illustrated in Caputo sense.HPTM is described to get the solution of the proposed model using the new kind of operator.Also,there are some analyses about the new kind of operator to prove the efficiency of the operator.
基金Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2024R229), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia。
文摘The current investigation examines the fractional forced Korteweg-de Vries(FF-KdV) equation,a critically significant evolution equation in various nonlinear branches of science. The equation in question and other associated equations are widely acknowledged for their broad applicability and potential for simulating a wide range of nonlinear phenomena in fluid physics, plasma physics, and various scientific domains. Consequently, the main goal of this study is to use the Yang homotopy perturbation method and the Yang transform decomposition method, along with the Caputo operator for analyzing the FF-KdV equation. The derived approximations are numerically examined and discussed. Our study will show that the two suggested methods are helpful, easy to use, and essential for looking at different nonlinear models that affect complex processes.
文摘This paper presents a study of nonlinear waves in shallow water.The Korteweg-de Vries(KdV)equa-tion has a canonical version based on oceanography theory,the shallow water waves in the oceans,and the internal ion-acoustic waves in plasma.Indeed,the main goal of this investigation is to employ a semi-analytical method based on the homotopy perturbation transform method(HPTM)to obtain the numerical findings of nonlinear dispersive and fifth order KdV models for investigating the behaviour of magneto-acoustic waves in plasma via fuzziness.This approach is connected with the fuzzy generalized integral transform and HPTM.Besides that,two novel results for fuzzy generalized integral transforma-tion concerning fuzzy partial gH-derivatives are presented.Several illustrative examples are illustrated to show the effectiveness and supremacy of the proposed method.Furthermore,2D and 3D simulations de-pict the comparison analysis between two fractional derivative operators(Caputo and Atangana-Baleanu fractional derivative operators in the Caputo sense)under generalized gH-differentiability.The projected method(GHPTM)demonstrates a diverse spectrum of applications for dealing with nonlinear wave equa-tions in scientific domains.The current work,as a novel use of GHPTM,demonstrates some key differ-ences from existing similar methods.
文摘In this study,by means of homotopy perturbation method(HPM) an approximate solution of the magnetohydrodynamic(MHD) boundary layer flow is obtained.The main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to solve.HPM produces analytical expressions for the solution to nonlinear differential equations.The obtained analytic solution is in the form of an infinite power series.In this work,the analytical solution obtained by using only two terms from HPM solution.Comparisons with the exact solution and the solution obtained by the Pade approximants and shooting method show the high accuracy,simplicity and efficiency of this method.
基金Project supported by the National Natural Science Foundation of China (No. 10561151)the Basic Science Research Fund in the Universities Directly Under the Inner Mongolia Autonomous Region(No. JY20220003)the Scientific Research Project of Hetao College of China (No. HYZQ202122)。
文摘In this paper, the time-fractional coupled viscous Burgers' equation(CVBE)and Drinfeld-Sokolov-Wilson equation(DSWE) are solved by the Sawi transform coupled homotopy perturbation method(HPM). The approximate series solutions to these two equations are obtained. Meanwhile, the absolute error between the approximate solution given in this paper and the exact solution given in the literature is analyzed. By comparison of the graphs of the function when the fractional order α takes different values, the properties of the equations are given as a conclusion.
文摘The entropy analysis of viscoelastic fluid obeying the simplified Phan-ThienTanner(SPTT)model with variable thermophysical properties are obtained for laminar,steady state and fully developed Couette-Poiseuille flow.The homotopy perturbation method(HPM)allows us to solve nonlinear momentum and energy differential equations.The Reynold’s model is used to describe the temperature dependency of thermophysical properties.Results indicate that the increase of the group parameter(Br=U)and the Brinkman number(Br)which show the power of viscous dissipation effect;increases the entropy generation while increasing fluid elasticity(εDe2)decreases the generated entropy.Increasing the Reynolds variational parameter(a)which control the level of temperature dependence of physical properties attenuate entropy generation when moving plate and applied pressure gradient have the opposite direction and decreases entropy generation when moving plate and applied pressure gradient have the same direction or both plates are at rest.Also,increasing elasticity reduces the difference between variable and constant thermophysical properties cases.These results may give guidelines for cost optimization in industrial processes.
文摘The dynamics of a spacecraft propelled by a continuous radial thrust resembles that of a nonlinear oscillator.This is analyzed in this work with a novel method that combines the definition of a suitable homotopy with a classical perturbation approach,in which the low thrust is assumed to be a perturbation of the nominal Keplerian motion.The homotopy perturbation method provides the analytical(approximate)solution of the dynamical equations in polar form to estimate the corresponding spacecraft propelled trajectory with a short computational time.The accuracy of the analytical results was tested in an orbital-targeting mission scenario.
文摘In this study,we investigate the seventh-order nonlinear Caputo time-fractional KdV equation.The suggested model's solutions,which have a series form,are obtained using the hybrid ZZ-transform under the aforementioned fractional operator.The proposed approach combines the homotopy perturbation method(HPM)and the ZZ-transform.We consider two specific examples with suitable initial conditions and find the series solution to test their applicability.To demonstrate the utility of the presented technique,we explore its applications to the fractional Sawada–Kotera–Ito problem and the Lax equation.We observe the impact of a few fractional orders on the wave solution evolution for the problems under consideration.We provide the efficiency and reliability of the ZZHPM by calculating the absolute error between the series solution and the exact solution of both the Sawada–Kotera–Ito and Lax equations.The convergence and uniqueness of the solution are portrayed via fixed-point theory.
文摘In this article comparative analysis of various semi-numerical schemes has beenmade for the case of squeezing flow of an incompressible viscous fluid between two largeparallel plates having no-slip at the boundaries.The medium of flow contains magnetohy-drodynamic(MHD)effect and having small pores.Modeled boundary value problem is solvedanalytically using Optimal homotopy asymptotic method(OHAM),homotopy perturbationmethod(HPM),differential transform method(DTM),Daftardar Jafari method(DIM)andAdomian decomposition method(ADM).For comparison purpose,residuals of these schemeshave been found and analyzed for accuracy.Analytical study indicates that DTM and DJM arequite good in tem of accuracy near the center of domain[—1,1]but the accuracy reducesconsiderably near the start and end of the given interval.HPM and OHAM residuals indicatethat OHAM surpasses HPM in terms of accuracy in the present case.
文摘We have analyzed an incompressible Sisko fluid through an axisymmetric uniform tube with a sinusoidal wave propagating down its walls. The present analysis of non- Newtonian fluid is investigated under the considerations of long wavelength and low Reynolds number approximation. The analytic solution is obtained using （i） the regular perturbation method （ii） the Homotopy analysis method （HAM）. The comparison of both the solutions is presented graphically. The results for the pressure rise, frictional force and pressure gradient have been calculated numerically and the results are studied for various values of the physical parameters of interest, such as α （angle of inclination）, b^＊ （Sisko fluid parameter）, Ф （amplitude ratio） and n （power law index）. Trapping phenomena is discussed at the end of the article.
基金funded by“Taif University Researchers Supporting Project Number(TURSP-2020/16),Taif University,Taif,Saudi Arabia.”。
文摘The development of mathematical modeling of infectious diseases is a key research area in various elds including ecology and epidemiology.One aim of these models is to understand the dynamics of behavior in infectious diseases.For the new strain of coronavirus(COVID-19),there is no vaccine to protect people and to prevent its spread so far.Instead,control strategies associated with health care,such as social distancing,quarantine,travel restrictions,can be adopted to control the pandemic of COVID-19.This article sheds light on the dynamical behaviors of nonlinear COVID-19 models based on two methods:the homotopy perturbation method(HPM)and the modied reduced differential transform method(MRDTM).We invoke a novel signal ow graph that is used to describe the COVID-19 model.Through our mathematical studies,it is revealed that social distancing between potentially infected individuals who are carrying the virus and healthy individuals can decrease or interrupt the spread of the virus.The numerical simulation results are in reasonable agreement with the study predictions.The free equilibrium and stability point for the COVID-19 model are investigated.Also,the existence of a uniformly stable solution is proved.
文摘Analytical and numerical analyses have performed to study the problem of the flow of incompressible Newtonian fluid between two parallel plates approaching or receding from each other symmetrically.The Navier–Stokes equations have been transformed into an ordinary differential equation using a similarity transformation.The powerful analytical methods called collocation method(CM),the homotopy perturbation method(HPM),and the homotopy analysis method(HAM)have been used to solve nonlinear differential equations.It has been attempted to show the capabilities and wide-range applications of the proposed methods in comparison with a type of numerical analysis as fourth-order Runge–Kutta numerical method in solving this problem.Also,velocity fields have been computed and shown graphically for various values of physical parameters.The objective of the present work is to investigate the effect of Reynolds number and suction or injection characteristic parameter on the velocity field.
