Numerical approximation of nonlinear stochastic Volterra integral equation based on Walsh function

Prit Pritam Paikaray ^[2] ; Nigam Chandra Parida ^[2] ; Sanghamitra Beuria ^[2] ; Omid Nikan ^[1]
1. [1] Iran University of Science and Technology
  
  Iran University of Science and Technology
  
  Irán
2. [2] Department of Mathematics, College of Basic Science and Humanities, OUAT, Bhubaneswar
Localización: SeMA Journal: Boletín de la Sociedad Española de Matemática Aplicada, ISSN-e 2254-3902, ISSN 2254-3902, Vol. 81, Nº. 4, 2024, págs. 665-678
Idioma: inglés
DOI: 10.1007/s40324-023-00341-5
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Resumen
- This paper adopts a highly effective numerical approach for approximating non-linear stochastic Volterra integral equations (NLSVIEs) based on the operational matrices of the Walsh function and the collocation method. The method transforms the integral equation into a system of algebraic equations, which allows for the derivation of an approximate solution. Error analysis is performed, confirming the effectiveness of the proposed method, which results in a linear order of convergence. Numerical examples are provided to illustrate the precision and effectiveness of the proposed method.