The Solution of Diffusion And Exothermic Zero Equation By Using Newton – Kantorovich Method

Abstract

This paper aims to a solution of a diffusion and exothermic equation by using Newton- Kantorovich method . The Newton- Kantorovich method is used to convert the nonlinear boundary value problem into linear boundary value problem , and then using numerical method to solve the linear boundary value problem .
The numerical method is a suitable based on a finite – difference method ( the central-difference ) scheme was considered here in since it gave a good results and thus obtaining small errors . The central- difference method is preferable over backward or forward difference scheme. Finally ,some numerical examples show that in this paper the results of proposed methods have a good agreement compared with that of exact solution . The use of finite- difference method produced a system of linear algebraic equations which are solved by using the Matlab computer software .