Physikalische Mathematik

A Second Order Accurate Difference Scheme for the Diffusion Equation with Nonlocal Nonlinear Boundary Conditions

Abstract

Abdelfatah Bouziani1*, Souad Bensaid and Sofiane Dehilis

This paper is considred to solve one-dimensional diffusion equation with nonlinear nonlocal boundary conditions. For the interior part of the problem, our discrete methods use the Forward time centred space (FTCS-NNC), Dufort–Frankel scheme (DFS-NNC), Backward time centred space (BTCS-NNC), Crank-Nicholson method (CNM-NNC), respectively. The integrals in the boundary equations are approximated by the trapezoidal rule. Here nonlinear terms are approximated by Richtmyer’s linearization method. The new algorithm are tested on two problems to show the effciency and accuracy of the schemes.