Analytical and Numerical Solutions for a Class of Nonlocal Nonlinear Parabolic Differential Equations

Abstract

The aim of this paper is to study a class of nonlocal nonlinear parabolic boundary value problems. First the existence, uniqueness, and continuous dependence of the solution upon the data are demonstrated, and then finite difference methods, backward Euler and Crank–Nicolson schemes are studied. It is proved that both numerical schemes are stable and convergent to the real solution. The results of some numerical examples are presented, which demonstrate the efficiency and rapid convergence of the methods.