<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>We consider the development of the direct method for the numerical solution of second order differential equations and corresponding initial value problems. Our technique based on the method of finite difference approximations. We obtain a quadratic order accurate an explicit method using the set of initial conditions in a natural way and approximations for the approximate numerical solution after the discretization of the continuous problem under appropriate conditions. We discuss the development of the method and the periodic property of the solution of the problem. In the numerical experiment, we consider both linear and nonlinear model problems to test the efficiency and accuracy of the method. The tabulated numerical results in computational experiments approve the quadratic order accuracy and efficiency of the method.</p>
</abstract>

We consider the development of the direct method for the numerical solution of second order differential equations and corresponding initial value problems. Our technique based on the method of finite difference approximations. We obtain a quadratic order accurate an explicit method using the set of initial conditions in a natural way and approximations for the approximate numerical solution after the discretization of the continuous problem under appropriate conditions. We discuss the development of the method and the periodic property of the solution of the problem. In the numerical experiment, we consider both linear and nonlinear model problems to test the efficiency and accuracy of the method. The tabulated numerical results in computational experiments approve the quadratic order accuracy and efficiency of the method.

An explicit second order uniformly convergent difference algorithm for an initial value problem associated to second order differential equations

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We consider the development of the direct method for the numerical solution of second order differential equations and corresponding initial value problems....

An explicit second order uniformly convergent difference algorithm for an initial value problem associated to second order differential equations

Published Online: Jun 20, 2022

Page range: 126 - 136

DOI: https://doi.org/10.2478/awutm-2022-0010

Keywords
Explicit method, Finite difference method, Nonlinear problem, Periodic property, Quadratic order Phase-lag

© 2022 Pramod Kumar Pandey et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

An explicit second order uniformly convergent difference algorithm for an initial value problem associated to second order differential equations

Published Online: Jun 20, 2022

Page range: 126 - 136

DOI: https://doi.org/10.2478/awutm-2022-0010

KeywordsExplicit method, Finite difference method, Nonlinear problem, Periodic property, Quadratic order Phase-lag

© 2022 Pramod Kumar Pandey et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Explicit method, Finite difference method, Nonlinear problem, Periodic property, Quadratic order Phase-lag