Legendre wavelets Galerkin method for solving nonlinear stochastic integral equations

Heydari, Mohammad Hossein; Hooshmandasl, Mohammad Reza; Shakiba, Ali; Cattani, Carlo

doi:10.1007/s11071-016-2753-x

Cited by 41 publications

(9 citation statements)

References 40 publications

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“…In the past several decades, researchers have developed various efficient 40 S. RAJA BALACHANDAR, D. UMA, S.G. VENKATESH, AND H. JAFARI numerical techniques for the same. Wavelet techniques using Haar wavelets, Legendre wavelets, Boubaker wavelets [1,10,30], polynomial approximation methods using Legendre polynomials [24] and operational matrix methods using block pulse function [23] are a few among many.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Singular Stochastic Integral Equations of Abel’s Type Using Operational Matrix Method

2022

Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan

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This paper proposes the orthogonal shifted Legendre collocation method to obtain an approximate solution for Abel-type singular linear stochastic integral equation. Our proposed method converts the singular linear stochastic equation to a system of algebraic equations. The shifted Legendre polynomials are used to obtain the operational matrices for such a conversion. The main advantage of the proposed method is that a sparse, tridiagonal orthogonal matrix is obtained, thus making process simple and efficient. The convergence and error analysis of the proposed method are discussed. Numerical examples prove the applicability and the efficiency of our proposed method.

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Section: Introductionmentioning

confidence: 99%

Numerical Solution of Singular Stochastic Integral Equations of Abel’s Type Using Operational Matrix Method

2022

Proceedings of the Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan

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“…al. (2014)], m-dimensional stochastic Itô-Volterra integral equations ], stochastic Volterra-Fredholm integral equations [Khodabin, M. et al (2012)], nonlinear stochastic Itô Volterra integral equations [Hashemi, B. et al (2017)], two-dimensional linear stochastic Volterra-Fredholm integral equation [Fallahpour, M. et al (2016)], stochastic Volterra integral equations [Shekarabi, F. H. et al (2014)], stochastic Volterra integral equations [Khodabin, M. et al (2014)], stochastic Itô-Volterra integral equations [Heydari, M. H. et al (2014)], reconditined semilinear stochastic singular and hypersingular integral equations [Rostami Varnos Fadrani, D., Maleknejad, K. (2000)], fractional stochastic integro-differential equation ], two dimensional linear stochastic integral equations on non-rectangular domains [Mirzaee, F., Samadyar, N. (2018)], Legendre wavelets Galerkin method for solving nonlinear stochastic integral equations [Heydari, M. H. et al (2016)], nonlinear Stratonovich Volterra integral equations ].…”

Section: Introductionmentioning

confidence: 99%

Bernstein polynomial multiwavelets operational matrices method for the numerical solution of system of linear Stratonovich Volterra integral equations

Shiralashetti¹,

Lamani²

2021

JSR

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This article gives an effective strategy to solve the system of linear Stratonovich Volterra integral equations. Using the Bernstein polynomial multiwavelets operational matrix of integration and its stochastic operational matrix of integration, the system of linear Stratonovich Volterra integral equations can be reduced to a system of linear algebraic equations with unknown coefficients, and the obtained linear algebraic equations are solved numerically. Error analysis of the proposed method is given. Numerical examples are presented to show that the method described is accurate and precise. Keywords-Bernstein polynomials, Bernstein polynomial multiwavelets, Brownian motion, Stratonovich Volterra integral equations, Stochastic operational matrix of integration of Bernstein polynomial multiwavelets.

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“…In general, these systems cannot be solved analytically; therefore, it is necessary to provide some appropriate numerical techniques for finding their approximate solutions. Recently, several numerical techniques are provided to solve the system of stochastic integral equations such as generalized hat functions method, block pulse functions method, collocation method based on the Bernstein polynomials, and Legendre wavelets Galerkin method …”

Section: Introductionmentioning

confidence: 99%

Convergence analysis of an iterative algorithm to solve system of nonlinear stochastic Itô‐Volterra integral equations

Saffarzadeh

Heydari

Loghmani

2020

Math Methods in App Sciences

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In this paper, an efficient and accurate numerical iterative algorithm based on the linear spline interpolation for solving the system of nonlinear stochastic Itô-Volterra integral equations is presented. The most important merit of this method is that it does not need to solve any system of nonlinear algebraic equations. An upper bound for the linear spline approximation of the stochastic function is provided. Using this upper bound and under the Lipschitz and linear growth conditions, the convergence analysis of the suggested method is studied.Finally, to verify the efficiency of the proposed scheme, some problems in the finance, physics, and biology are investigated, and the obtained results are compared with the stochastic -method. KEYWORDSlinear spline interpolation, multiple stock models, pendulum problem, predator-prey models, successive approximations method, system of stochastic Volterra integral equations MSC CLASSIFICATION 60H10; 60H20; 65C30Math Meth Appl Sci. 2020;43:5212-5233. wileyonlinelibrary.com/journal/mma

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Legendre wavelets Galerkin method for solving nonlinear stochastic integral equations

Cited by 41 publications

References 40 publications

Numerical Solution of Singular Stochastic Integral Equations of Abel’s Type Using Operational Matrix Method

Numerical Solution of Singular Stochastic Integral Equations of Abel’s Type Using Operational Matrix Method

Bernstein polynomial multiwavelets operational matrices method for the numerical solution of system of linear Stratonovich Volterra integral equations

Convergence analysis of an iterative algorithm to solve system of nonlinear stochastic Itô‐Volterra integral equations

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