Approximate solution of two dimensional linear and nonlinear stochastic Itô–Volterra integral equations via meshless scheme

Solhi, Erfan; Mirzaee, Farshid; Naserifar, Shiva

doi:10.1016/j.matcom.2023.01.009

Cited by 17 publications

(1 citation statement)

References 23 publications

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“…For this reason, numerical methods are used as a useful tool to solve them. For instance, see earlier research [17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

A projection method based on the piecewise Chebyshev cardinal functions for nonlinear stochastic ABC fractional integro‐differential equations

Heydari,

Zhagharian,

Cattani

2024

Math Methods in App Sciences

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In this study, the Atangana–Baleanu fractional derivative in the Caputo type (as a kind of non‐local and non‐singular derivative) is used to define a new class of stochastic fractional integro‐differential equations. A projection method (more precisely, a Galerkin approach) based on the piecewise Chebyshev cardinal functions is developed to solve these stochastic fractional equations. To construct this method, the operational matrices of fractional and stochastic integrals of these basis functions are obtained and used in the established method. By approximating the solution of the problem with a finite expansion of the expressed basis functions (in which the expansion coefficients are unknown), a system of algebraic equations is obtained. By solving this system, the expansion coefficients and subsequently the solution of the original stochastic fractional problem are obtained. The convergence analysis of the proposed method is investigated, theoretically and numerically. The accuracy of the established procedure is illustrated by solving several numerical examples.

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“…For this reason, numerical methods are used as a useful tool to solve them. For instance, see earlier research [17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

A projection method based on the piecewise Chebyshev cardinal functions for nonlinear stochastic ABC fractional integro‐differential equations

Heydari,

Zhagharian,

Cattani

2024

Math Methods in App Sciences

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Orthonormal discrete Legendre polynomials for stochastic distributed‐order time‐fractional fourth‐order delay sub‐diffusion equation

Heydari,

Razzaghi

2024

Math Methods in App Sciences

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In this study, the stochastic distributed‐order time‐fractional version of the fourth‐order delay sub‐diffusion equation is defined by employing the Caputo fractional derivative. The orthonormal discrete Legendre polynomials, as a well‐known family of discrete polynomials basis functions, are used to develop a numerical method to solve this equation. To employ these polynomials in constructing the expressed approach, the operational matrices of the classical integration, differentiation (ordinary, fractional and distributed‐order fractional), and stochastic integration of these polynomials are extracted. The established method turns solving the introduced stochastic‐fractional equation into solving a more simple linear algebraic system of equations. In fact, by representing the unknown solution in terms of the introduced polynomials and employing the extracted matrices, this system is obtained. The accuracy of the developed algorithm is numerically checked by solving two examples.

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Lagrange interpolation polynomials for solving nonlinear stochastic integral equations

Boukhelkhal,

Zeghdane

2023

Numer Algor

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Approximate solution of two dimensional linear and nonlinear stochastic Itô–Volterra integral equations via meshless scheme

Cited by 17 publications

References 23 publications

A projection method based on the piecewise Chebyshev cardinal functions for nonlinear stochastic ABC fractional integro‐differential equations

A projection method based on the piecewise Chebyshev cardinal functions for nonlinear stochastic ABC fractional integro‐differential equations

Orthonormal discrete Legendre polynomials for stochastic distributed‐order time‐fractional fourth‐order delay sub‐diffusion equation

Lagrange interpolation polynomials for solving nonlinear stochastic integral equations

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