THE IMPLICIT DIFFERENCE SCHEME FOR THE NONLINEAR PARABOLIC EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS
带非局部边界条件的非线性抛物方程的隐式差分解法

Parabolic equations with nonlocal boundary conditions arise from quasi-static elasticity, electrochemistry and etc. In this paper, we construct an implicit finite difference scheme for the nonlinear parabolic equation with nonlocal boundary conditions. Moreover, using the discrete functional analysis and the fixed-point theorem, we prove that the numerical solution is exist and convergent with the convergence order $O(\tau +h^2)$ in the $L_{\infty}$-norm. Numerical examples are given to illustrate the theoretical results.