Numerical solutions of a class of non-linear ordinary differential equations in Hermite series
No Thumbnail Available
Date
2019
Journal Title
Journal ISSN
Volume Title
Abstract
The purpose of this paper is to present a Hermite polynomial approach for solving a high-order ODE with non-linear terms under mixed conditions. The method we used is a matrix method based on collocation points together with truncated Hermite series and reduces the solution of equation to solution of a matrix equation which corresponds to a system of non-linear algebraic equations with unknown Hermite coefficients. In addition, to illustrate the validity and applicability of the method, some numerical examples together with residual error analysis are performed and the obtained results are compared with the existing result in literature. © 2019 Society of Thermal Engineers of Serbia.
Description
Keywords
Linear equations , Matrix algebra , Numerical methods , Polynomials , Collocation method , Hermite series , Hermite's polynomials , High-order ODEs , Matrix methods , Non linear , Non-linear ODE , Nonlinear ordinary differential equation , Numerical solution , Polynomial approach , Ordinary differential equations