Approximate solution of stochastic Volterra integro-differential equations by using moving least squares scheme and spectral collocation method

Farshid Mirzaee, Erfan Solhi and Shiva Naserifar

Applied Mathematics and Computation, 2021, vol. 410, issue C

Abstract: In this paper, an attractive idea using moving least squares (MLS) and spectral collocation method is extended to estimate the solution of nonlinear stochastic Volterra integro-differential equations (NSVIDEs) that arise in mathematical modeling of natural systems in financial mathematics, physics, and engineering. An essential advantage of the proposed technique is that it does not require any preprocessing, such as mesh refinement. Another advantage that may be appealing to the readers of this article is that acceptable results can be obtained using a small number of points and basis functions, so the calculations are reduced. Applying the proposed scheme leads to the conversion of the problem into a system of algebraic equations. An error bound is presented to ensure the convergence and reliability of the method. Some illustrative examples are presented to reveal the efficiency and applicability of this technique.

Keywords: Stochastic Volterra integro-differential equations; Nonlinear integral equations; Spectral collocation method; Brownian motion process; Moving least squares (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:410:y:2021:i:c:s0096300321005361

DOI: 10.1016/j.amc.2021.126447

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