10.1007/s40096-018-0269-x

A computational method for solving stochastic Itô–Volterra integral equation with multi-stochastic terms

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  • N. Momenzade1,
  • A. R. Vahidi*2,
  • E. Babolian2,
  1. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IR
  2. Department of Mathematics, College of Science, Yadegar-e-Emam Khomeyni (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, IR
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Published in Issue 2018-11-19

How to Cite

Momenzade, N., Vahidi, A. R., & Babolian, E. (2018). A computational method for solving stochastic Itô–Volterra integral equation with multi-stochastic terms. Mathematical Sciences, 12(4 (December 2018). https://doi.org/10.1007/s40096-018-0269-x
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Abstract

Abstract In this paper, a linear combination of quadratic modified hat functions is proposed to solve stochastic Itô–Volterra integral equation with multi-stochastic terms. All known and unknown functions are expanded in terms of modified hat functions and replaced in the original equation. The operational matrices are calculated and embedded in the equation to achieve a linear system of equations which gives the expansion coefficients of the solution. Also, under some conditions the error of the method is O(h3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(h^3)$$\end{document} . The accuracy and reliability of the method are studied and compared with those of block pulse functions and generalized hat functions in some examples.

Keywords

  • Modified hat functions,
  • Stochastic operational matrix,
  • Stochastic Itô–Volterra integral equation,
  • Brownian motion
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