A novel numerical approach based on shifted second-kind Chebyshev polynomials for solving stochastic Ito-Volterra integral equation of Abel type with weakly singular kernel
MATHEMATICAL METHODS IN THE APPLIED SCIENCES(2023)
摘要
In this paper, a collocation method based on shifted second-order Chebyshev polynomials is implemented to obtain the approximate solution of the stochastic Ito-Volterra integral equation of Abel type with weakly singular kernel. In this method, operational matrices are used to convert the stochastic Ito-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.
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关键词
Brownian motion,Chebyshev polynomial,collocation method,convergence analysis,error analysis,stochastic Ito-Volterra integral equation,Ito integral
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