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ADM–TF hybrid method for nonlinear Itô–Volterra integral equations

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  • Hashemi, Seyyed Amjad Samareh
  • Saeedi, Habibollah

Abstract

In this paper, a new combination method is being proposed for the numerical solution of nonlinear Itô–Volterra stochastic integral equations based on Adomian decomposition method (ADM), Triangular function (TF) approximation, quadrature methods and Itô stochastic integration formula. The presented method is developed in two steps. First, we apply ADM to the main equation then for calculating the components, we used TF-approximation together with quadrature and Itô stochastic integration formula. Some theorems related to error and convergence analysis of the suggested method are also stated. Finally, several examples confirm the applicability, efficiency and accuracy of the method, along with comparisons.

Suggested Citation

  • Hashemi, Seyyed Amjad Samareh & Saeedi, Habibollah, 2021. "ADM–TF hybrid method for nonlinear Itô–Volterra integral equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 783-798.
    • Handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:783-798
    DOI: 10.1016/j.matcom.2021.02.003
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