The homotopy perturbation method to solve initial valu problems of first order with discontinuities

الملخص EN

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, ||||2, maximum relative error, maximum residual error, and expected convergence order are also provided.