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

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Publicado en:SeMA Journal vol. 81, no. 4 (Dec 2024), p. 665
Autor principal: Paikaray, Prit Pritam
Otros Autores: Parida, Nigam Chandra, Beuria, Sanghamitra, Nikan, Omid
Publicado:
Springer Nature B.V.
Materias:
Mathematical functions
Approximation
Stochastic models
Error analysis
Walsh function
Integral equations
Brownian motion
Inequality
Volterra integral equations
Collocation methods
Effectiveness
Acceso en línea:Citation/Abstract
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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.
ISSN:2254-3902
2281-7875
1575-9814
1575-9822
DOI:10.1007/s40324-023-00341-5
Fuente:Science Database