Rigorous convergence analysis of Jacobi spectral Galerkin methods for Volterra integral equations with noncompact kernels

2020 ◽  
Vol 366 ◽  
pp. 112403 ◽  
Author(s):  
Yin Yang ◽  
Emran Tohidi ◽  
Xiaohua Ma ◽  
Sujuan Kang
Keyword(s):  
Convergence Analysis ◽  
Integral Equations ◽  
Volterra Integral Equations ◽  
Galerkin Methods ◽  
Spectral Galerkin Methods

Numerical Treatment of Nonlinear Stochastic Itô–Volterra Integral Equations by Piecewise Spectral-Collocation Method

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Fakhrodin Mohammadi
Keyword(s):  
Approximate Solution ◽  
Finite Number ◽  
Convergence Analysis ◽  
Integral Equations ◽  
Lagrange Interpolation ◽  
Interpolation Method ◽  
Approximate Solutions ◽  
Volterra Integral Equations ◽  
Numerical Treatment ◽  
Nonlinear Integral Equations

This paper deals with the approximate solution of nonlinear stochastic Itô–Volterra integral equations (NSIVIE). First, the solution domain of these nonlinear integral equations is divided into a finite number of subintervals. Then, the Chebyshev–Gauss–Radau points along with the Lagrange interpolation method are employed to get approximate solution of NSIVIE in each subinterval. The method enjoys the advantage of providing the approximate solutions in the entire domain accurately. The convergence analysis of the numerical method is also provided. Some illustrative examples are given to elucidate the efficiency and applicability of the proposed method.

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