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
Copyright policy )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
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.
Numerical solutions to stochastic differential and integral equations, Volterra integral equations, Itô integral, stochastic Itô-Volterra integral equation, Numerical methods for integral equations, Chebyshev polynomial, convergence analysis, collocation method, Brownian motion, Computational methods for stochastic equations (aspects of stochastic analysis), error analysis
Numerical solutions to stochastic differential and integral equations, Volterra integral equations, Itô integral, stochastic Itô-Volterra integral equation, Numerical methods for integral equations, Chebyshev polynomial, convergence analysis, collocation method, Brownian motion, Computational methods for stochastic equations (aspects of stochastic analysis), error analysis
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