This paper is concerned with the order of the solutions of systems of high-order complex algebraic differential equations.By means of Zalcman Lemma,the systems of equations of[1]is extended to more general form.
A wavelet method is proposed to solve the Burgers’equation.Following this method,this nonlinear partial differential equation is first transformed into a system of ordinary differential equations using the modified w...A wavelet method is proposed to solve the Burgers’equation.Following this method,this nonlinear partial differential equation is first transformed into a system of ordinary differential equations using the modified wavelet Galerkin method recently developed by the authors.Then,the classical fourth-order explicit Runge–Kutta method is employed to solve the resulting system of ordinary differential equations.Such a wavelet-based solution procedure has been justified by solving two test examples:results demonstrate that the proposed method has a much better accuracy and efficiency than many other existing numerical methods,and whose order of convergence can go up to 5.Most importantly,our results also indicate that the present wavelet method can readily deal with those fluid dynamics problems with high Reynolds numbers.展开更多
In this paper, we establish the product formula for the fixed point index on product cone, andthen, as applications, consider the existence, nonexistence and multiplicity of positive solutions for a second-order ordin...In this paper, we establish the product formula for the fixed point index on product cone, andthen, as applications, consider the existence, nonexistence and multiplicity of positive solutions for a second-order ordinary differential system with parameters. The discussion is based on the product formula and thefundamental properties of the fixed point index.展开更多
By studying the spectrum of the underlying operator corresponding to the exhaustive-service M/G/1 queueing model with single vacations we prove that the time-dependent solution of the model strongly converges to its s...By studying the spectrum of the underlying operator corresponding to the exhaustive-service M/G/1 queueing model with single vacations we prove that the time-dependent solution of the model strongly converges to its steady-state solution.展开更多
Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditionalsymmetries (GCSs) is implemented.The reducibility of the initial-value problem for an evolution equation to a ...Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditionalsymmetries (GCSs) is implemented.The reducibility of the initial-value problem for an evolution equation to a Cauchyproblem for a system of ordinary differential equations (ODEs) is characterized via the GCS and its Lie symmetry.Complete classification theorems are obtained and some examples are taken to show the main reduction procedure.展开更多
In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from ...In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure- preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f . Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system.展开更多
This paper studies a class of forward-backward stochastic differential equations (FBSDE)in a general Markovian framework.The forward SDE represents a large class of strong Markov semimartingales,and the backward gener...This paper studies a class of forward-backward stochastic differential equations (FBSDE)in a general Markovian framework.The forward SDE represents a large class of strong Markov semimartingales,and the backward generator requires only mild regularity assumptions.The authors showthat the Four Step Scheme introduced by Ma,et al.(1994) is still effective in this case.Namely,the authors show that the adapted solution of the FBSDE exists and is unique over any prescribedtime duration;and the backward components can be determined explicitly by the forward componentvia the classical solution to a system of parabolic integro-partial differential equations.An importantconsequence the authors would like to draw from this fact is that,contrary to the general belief,in aMarkovian set-up the martingale representation theorem is no longer the reason for the well-posednessof the FBSDE,but rather a consequence of the existence of the solution of the decoupling integralpartialdifferential equation.Finally,the authors briefly discuss the possibility of reducing the regularityrequirements of the coefficients by using a scheme proposed by F.Delarue (2002) to the current case.展开更多
基金Supported by the Natural Science Foundation of Guangdong Province（04010474） Supported by the Foundation of the Education Department of Anhui Province for Outstanding Young Teachers in University（2011SQRL172）
文摘This paper is concerned with the order of the solutions of systems of high-order complex algebraic differential equations.By means of Zalcman Lemma,the systems of equations of[1]is extended to more general form.
基金Supported by the Funds of Ministry of Education of China for PhD Units under No. 200201410L3the National Natural Science Foundation of China under project grant No.10471015
基金supported by the National Natural Science Foundation of China(Grant Nos.11032006,11072094,and 11121202)the Ph.D.Program Foundation of Ministry of Education of China(Grant No.20100211110022)+2 种基金the National Key Project of Magneto-Constrained Fusion Energy Development Program(Grant No.2013GB110002)the Fundamental Research Funds for the Central Universities(Grant No.lzujbky-2013-1)the Scholarship Award for Excellent Doctoral Student granted by the Lanzhou University
文摘A wavelet method is proposed to solve the Burgers’equation.Following this method,this nonlinear partial differential equation is first transformed into a system of ordinary differential equations using the modified wavelet Galerkin method recently developed by the authors.Then,the classical fourth-order explicit Runge–Kutta method is employed to solve the resulting system of ordinary differential equations.Such a wavelet-based solution procedure has been justified by solving two test examples:results demonstrate that the proposed method has a much better accuracy and efficiency than many other existing numerical methods,and whose order of convergence can go up to 5.Most importantly,our results also indicate that the present wavelet method can readily deal with those fluid dynamics problems with high Reynolds numbers.
基金supported by Natural Science Foundation in Jiangsu Province (Grant Nos.10KJB110004, 08KJD110010)National Natural Science Foundation of China (Grant Nos. 10971046, 10831005, 10671195)China Postdoctoral Science Foundation (Grant Nos. 20090450601)
文摘In this paper, we establish the product formula for the fixed point index on product cone, andthen, as applications, consider the existence, nonexistence and multiplicity of positive solutions for a second-order ordinary differential system with parameters. The discussion is based on the product formula and thefundamental properties of the fixed point index.
基金supported by National Natural Science Foundation of China (GrantNo. 10861011)
文摘By studying the spectrum of the underlying operator corresponding to the exhaustive-service M/G/1 queueing model with single vacations we prove that the time-dependent solution of the model strongly converges to its steady-state solution.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10447007 and 10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.2005A13
文摘Symmetry reduction of a class of third-order evolution equations that admit certain generalized conditionalsymmetries (GCSs) is implemented.The reducibility of the initial-value problem for an evolution equation to a Cauchyproblem for a system of ordinary differential equations (ODEs) is characterized via the GCS and its Lie symmetry.Complete classification theorems are obtained and some examples are taken to show the main reduction procedure.
基金Supported by National Nature Science Foundation of China under Grant No. 10701081
文摘In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure- preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f . Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system.
基金supported by the National Science Foundation under Grant Nos. #DMS 0505472, 0806017,and#DMS 0604309
文摘This paper studies a class of forward-backward stochastic differential equations (FBSDE)in a general Markovian framework.The forward SDE represents a large class of strong Markov semimartingales,and the backward generator requires only mild regularity assumptions.The authors showthat the Four Step Scheme introduced by Ma,et al.(1994) is still effective in this case.Namely,the authors show that the adapted solution of the FBSDE exists and is unique over any prescribedtime duration;and the backward components can be determined explicitly by the forward componentvia the classical solution to a system of parabolic integro-partial differential equations.An importantconsequence the authors would like to draw from this fact is that,contrary to the general belief,in aMarkovian set-up the martingale representation theorem is no longer the reason for the well-posednessof the FBSDE,but rather a consequence of the existence of the solution of the decoupling integralpartialdifferential equation.Finally,the authors briefly discuss the possibility of reducing the regularityrequirements of the coefficients by using a scheme proposed by F.Delarue (2002) to the current case.
