AL-Rafidain Journal of Computer Sciences and Mathematics

Abstract

In this work, the homotopy perturbation method (HPM) is used to solve initial value
problems of first order with various types of discontinuities. The numerical results obtained (are
compared) using the traditional HPM, and the integral equation of the nth equation with the
solution numerical obtained using Simpson and Trapezoidal Rules to demonstrate that the
solution results are extremely accurate when compared to the exact solution. The maximum
absolute error, ‖ . ‖ , maximum relative error, maximum residual error, and expected
convergence order are also provided.