Approximate Solution of an Integrodifferential Equation Generalized by Harry Dym Equation Using the Picard Successive Method

Abstract

In this study, we discuss the approximate solution of the Harry Dym nonlinear partial differential equation and its integrodifferential version. We first construct the Picard successive approximation for the equations under consideration. Then, we give a detailed calculation of the approximate solution for two cases of the partial Harry Dym integrodifferential equation. The approximate solutions are illustrated for some chosen values of the arbitrary constants. The efficiency of this semianalytical method is demonstrated through discussing the regions of the domain with small errors as well as by extracting the exact solution from the limit of the approximation.