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Casasús, L. and Al-Hayani, W. (2002) The Decomposition Method for Ordinary Differential Equations with Discontinuities. Applied Mathematics and Computation, 131, 245-251.
https://doi.org/10.1016/s0096-3003(01)00142-4

has been cited by the following article:

• 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.