Numerical solution of stochastic Itô-Volterra integral equation by using Shifted Jacobi operational matrix method

Ray, S. Saha; Singh, P. K.

doi:10.1016/j.amc.2021.126440

Cited by 6 publications

(1 citation statement)

References 17 publications

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“…To solve deterministic IEs or SIEs, a variety of numerical approaches are developed. Bernstien polynomials [8,9], orthonormal Bernoulli polynomials (OBPs) [10], block pulse functions [11], Chebyshev wavelets [12], Legendre polynomials [13], shifted Jacobi operational matrix [14], shifted Legendre polynomials [15], meshless local discrete Galerkin scheme [16], wavelets Galerkin method [17], generalized hat basis functions [18], Legendre wavelets Galerkin method [19], Chebyshev cardinal wavelets [20,21], and so on are utilized to determine the solution for different types of IEs.…”

Section: Introductionmentioning

confidence: 99%

A novel numerical approach based on shifted second‐kind Chebyshev polynomials for solving stochastic Itô–Volterra integral equation of Abel type with weakly singular kernel

Ray

Gupta

2023

Math Methods in App Sciences

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In this paper, a collocation method based on shifted second‐order Chebyshev polynomials is implemented to obtain the approximate solution of the stochastic Itô–Volterra integral equation of Abel type with weakly singular kernel. In this method, operational matrices are used to convert the stochastic Itô–Volterra integral equation to algebraic equations that are linear. The algorithm of the proposed numerical scheme has been presented in this paper. Also, the error bound and convergence of the proposed method are well established. Consequently, two illustrative examples are provided to demonstrate the efficiency, plausibility, reliability, and consistency of the current methodology.

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