Finite difference solutions for parabolic equations with the time weighting initial conditions

摘要

A class of nonlinear parabolic boundary value problems with time weighting initial condition is considered. Instead of studying the existence, uniqueness, and continuous dependence of the solution upon the data we give a brief review of the known results and then concentrate on the performance of the backward Euler and Crank-Nicolson finite difference schemes [1]. The results of some numerical examples are presented which demonstrate the efficiency and rapid convergence.