TITLE:
Homotopy Analysis Method for Solving Initial Value Problems of Second Order with Discontinuities
AUTHORS:
Waleed Al-Hayani, Rasha Fahad
KEYWORDS:
Homotopy Analysis Method, Initial Value Problems, Heaviside Step Function, Dirac Delta Function, Simpson Rule
JOURNAL NAME:
Applied Mathematics,
Vol.10 No.6,
June
17,
2019
ABSTRACT: In this paper, the standard homotopy analysis method was applied to initial value problems of the second order with some types of discontinuities, for both linear and nonlinear cases. To show the high accuracy of the solution results compared with the exact solution, a comparison of the numerical results was made applying the standard homotopy analysis method with the iteration of the integral equation and the numerical solution with the Simpson rule. Also, the maximum absolute error, , the maximum relative error, the maximum residual error and the estimated order of convergence were given. The research is meaningful and I recommend it to be published in the journal.