A Computational Approach for Constructing Singular Solutions of One-Dimensional Pseudoparabolic and Metaparabolic Equations

Abstract

In the present work a computational approach is developed for constructing singular solutions of the one-dimensional pseudoparabolic and metaparabolic equations. Recursive schemes are developed to determine expansion coefficients for the singularities. It is shown, furthermore, that the coefficients are themselves special solutions of ordinary differential equations. Closed form expressions are obtained for these coefficients using a symbolic and algebraic manipulation language. Several examples are provided to indicate the usefulness of this new approach to construct fundamental solutions.