10.1007/s40096-022-00502-z

A novel operational matrix method based on Genocchi polynomials for solving n-dimensional stochastic Itô–Volterra integral equation

  • P. K. Singh1,
  • S. Saha Ray*1,
  1. Department of Mathematics, National Institute of Technology, Rourkela, 769008, IN

Published in Issue 2022-12-17

How to Cite

Singh, P. K., & Saha Ray, S. (2022). A novel operational matrix method based on Genocchi polynomials for solving n-dimensional stochastic Itô–Volterra integral equation. Mathematical Sciences, 18(2 (June 2024). https://doi.org/10.1007/s40096-022-00502-z
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Abstract

Abstract A reliable numerical method has been presented in this article to solve n -dimensional stochastic Itô–Volterra integral equations. In the proposed approach, relying on the valuable properties of Genocchi polynomials, operational matrices and related coefficient matrix have been introduced to convert the n -dimensional stochastic Itô–Volterra integral equation into a linear or nonlinear algebraic equation. Then collocation points have been used to generate the system of algebraic equations, which can be further solved by Newton’s method. Also, convergence analysis of the discussed technique is established. Finally, few illustrative problems have been examined to prove the efficiency and accuracy of the proposed scheme.

Keywords

  • Genocchi polynomial,
  • Stochastic Itô–Volterra integral equations,
  • Itô integral,
  • Operational matrices,
  • Convergence analysis

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