The Homotopy Perturbation Method to Solve Initial Value Problems of First Order with Discontinuities

Abstract

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

Keywords

• homotopy perturbation method
• he’s polynomials
• initial value problems (ivps)
• unit step function
• unit impulse function
• simpson rule
• trapezoidal rule