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Generalized Jacobi Spectral-Galerkin Method for Nonlinear Volterra Integral Equations with Weakly Singular Kernels |
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| Authors: | Jie Shen Changtao Sheng & Zhongqing Wang |
| Abstract: | We propose a generalized Jacobi spectral-Galerkin method for the nonlinear Volterra integral equations (VIEs) with weakly singular kernels. We establish the existence and uniqueness of the numerical solution, and characterize the convergence of the proposed method under reasonable assumptions on the nonlinearity. We also present numerical results which are consistent with the theoretical predictions. |
| Keywords: | Generalized Jacobi spectral-Galerkin method nonlinear Volterra integral equations with weakly singular kernels convergence analysis |
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