Analysis of difference approximations to delay pseudo-parabolic equations

Abstract

This work deals with the one-dimensional initial-boundary Sobolev or pseudo-parabolic problem with delay. For solving this problem numerically, we construct fourth-order difference-differential scheme and obtain the error estimate for its solution. Further, for the time variable, we use the appropriate Runge–Kutta method for the realization of our differential-difference problem. Numerical results supporting the theory are presented.