Modified Crank-Nicholson difference schemes for ultra parabolic equations with Neumann condition

Abstract

In this paper, our interest is studying the stability of difference schemes for the approximate solution of the initial boundary value problem for ultra-parabolic equations. For approximately solving the given problem, the second-order of accuracy modified Crank-Nicholson difference schemes are presented. Theorem on almost coercive stability of these difference schemes is established. Numerical example is given to illustrate the applicability and efficiency of our method. © 2013 Springer-Verlag.