To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’...To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.展开更多
In the paper [1], authors have suggested and analyzed a predictor-corrector Halley method for solving nonlinear equations. In this paper, we modified this method by using the finite difference scheme, which had a quan...In the paper [1], authors have suggested and analyzed a predictor-corrector Halley method for solving nonlinear equations. In this paper, we modified this method by using the finite difference scheme, which had a quantic convergence. We have compared this modified Halley method with some other iterative methods of ninth order, which shows that this new proposed method is a robust one. Some examples are given to illustrate the efficiency and the performance of this new method.展开更多
The paper addresses the question of optimal development of a developing economy. The framework presented, it is believed, can be of help in thinking about policies relating, inter alia, to population growth, inter-sec...The paper addresses the question of optimal development of a developing economy. The framework presented, it is believed, can be of help in thinking about policies relating, inter alia, to population growth, inter-sectoral migration, agriculture-industry relationship, wages in different sectors, and income distribution in an inter-connected way in the context of optimal development of an economy with an informal sector.展开更多
In this paper, the inverse problem for the viscoelastic medium is investigated in the time domain, in which the wave impedance of the medium is discontinuous at the rear interface. The differentio-integral equations g...In this paper, the inverse problem for the viscoelastic medium is investigated in the time domain, in which the wave impedance of the medium is discontinuous at the rear interface. The differentio-integral equations governing the behavior of the scattering and propagation operators are utilized to reconstruct the relaxation modulus of the viscoelastic medium. A new approach, in which only the one-side measurement reflection data for one round trip through the viscoelastic layer, is developed. The numerical examples are given at the end of the paper. Ir is shown that the curves of the reconstructed moduli coincide very well with the original relaxation moduli.展开更多
文摘To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.
文摘In the paper [1], authors have suggested and analyzed a predictor-corrector Halley method for solving nonlinear equations. In this paper, we modified this method by using the finite difference scheme, which had a quantic convergence. We have compared this modified Halley method with some other iterative methods of ninth order, which shows that this new proposed method is a robust one. Some examples are given to illustrate the efficiency and the performance of this new method.
文摘The paper addresses the question of optimal development of a developing economy. The framework presented, it is believed, can be of help in thinking about policies relating, inter alia, to population growth, inter-sectoral migration, agriculture-industry relationship, wages in different sectors, and income distribution in an inter-connected way in the context of optimal development of an economy with an informal sector.
文摘In this paper, the inverse problem for the viscoelastic medium is investigated in the time domain, in which the wave impedance of the medium is discontinuous at the rear interface. The differentio-integral equations governing the behavior of the scattering and propagation operators are utilized to reconstruct the relaxation modulus of the viscoelastic medium. A new approach, in which only the one-side measurement reflection data for one round trip through the viscoelastic layer, is developed. The numerical examples are given at the end of the paper. Ir is shown that the curves of the reconstructed moduli coincide very well with the original relaxation moduli.
