NUMERICAL SOLUTION FOR ANTI-PERSISTENT PROCESS BASED STOCHASTIC INTEGRAL EQUATIONS

In this article, we propose the shifted Legendre polynomial solutions for anti-persistent process based stochastic integral equations. The operational matrices for stochastic integration and fractional stochastic integration are efficiently generated using the properties of shifted Legendre polynomi...

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Bibliographic Details
Published inTWMS journal of applied and engineering mathematics Vol. 14; no. 1; p. 368
Main Authors Balachandar, S.R, Venkatesh, S.G
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.01.2024
Elman Hasanoglu
Subjects
Approximation
Brownian motion
Error functions
Exact solutions
Integral equations
Management science
Mathematical analysis
Mathematical functions
Mathematics
Numerical analysis
Polynomials
Simultaneous equations
Stochastic models
Time series
Upper bounds
India
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Summary:In this article, we propose the shifted Legendre polynomial solutions for anti-persistent process based stochastic integral equations. The operational matrices for stochastic integration and fractional stochastic integration are efficiently generated using the properties of shifted Legendre polynomials. In addition, the original problem can be reduced to a system of simultaneous equations with (N + 1) unknowns in the function approximation. By solving the given stochastic integral equations, we obtain numerical solutions. The proposed method's convergence is derived in terms of the error function's expectation, and the upper bound of the error in [L.sup.2] norm is also discussed in detail. The applicability of this methodology is demonstrated using numerical examples and the solution's quality is statistically validated by comparing it with the exact solution. Keywords: Stochastic Ito Volterra integral equation, Shifted Legendre polynomial, Stochastic operational matrix, Convergence analysis, Error estimation. AMS Subject Classification: Primary 65C30, 60G42, 60H35, 60H10, 65C20; Secondary 60H20, 68U20.
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content type line 14
ISSN:2146-1147
2146-1147