On the numerical solution of pseudoparabolic equations

Abstract

In this work the authors find discrete analogues of the fundamental singularities for pseudo-parabolic equations. The method developed by Colton and Gilbert for analytic coefficients is used to motivate the approach. Indeed, the finite difference Green’s function is seen to play the same role here as in the analytic case. The method of lines is employed to treat the time differentiation. Furthermore, error estimates are obtained which compare the continuous solutions to the finite difference approximations.