NUMERICAL SOLUTION FOR ANTI-PERSISTENT PROCESS BASED STOCHASTIC INTEGRAL EQUATIONS - Balachandar, S.R; Venkatesh, S.G (TWMS journal of applied and engineering mathematics, 2024)
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.