Numerical Solution of a Nonlinear Diffusion Model with Memory

Abstract

Finite difference approximation of a nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. Here we discuss the model described by a nonlinear integro-differential equation. The system of time dependent ordinary differential equations is solved using Runge-Kutta method with adaptive step size. The time integral make this a non-trivial application of the Matlab code ODE45. Eight examples are given with mostly homogeneous boundary conditions. The results show that when the analytic solution is not growing in time, then the solution decays at a rate proven theoretically in the literature.