An efficient numerical method based on Lucas polynomials to solve multi-dimensional stochastic Itô-Volterra integral equations

P.K. Singh and S. Saha Ray

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 203, issue C, 826-845

Abstract: This article discusses the operational matrix method relying on Lucas polynomial to find the solution of multi-dimensional stochastic Itô-Volterra integral equation. For that purpose, the properties of Lucas polynomial and operational matrices have been investigated. Using Lucas polynomial based functions approximations and operational matrices along with collocation points, the multi-dimensional stochastic Itô-Volterra integral equation is converted into a linear or nonlinear system of algebraic equations. Convergence analysis of the presented method has been discussed. Numerical examples are examined to show their computational efficiency and accuracy.

Keywords: Lucas polynomial; Itô integral; Multi-dimensional stochastic Itô-Volterra integral equations; Operational matrices; Convergence analysis (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:203:y:2023:i:c:p:826-845

DOI: 10.1016/j.matcom.2022.06.029

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