Abstract

In this work, a first order and second order difference schemes, namely Rothe and Crank-Nicholson, respectively, for solving nonlocal boundary value problems for parabolic differential equations are presented. The stability of the difference schemes are proved by using the matrix stability approach. Numerical results are provided to illustrate the accuracy and efficiency of the schemes. 

Key words: Matrix stability, Rothe difference scheme, Crank-Nicholson difference scheme, Kailath Theorem, nonlocal boundary value problems for parabolic differential equations, Schur complement, matrix block inversion.