Generalized Jacobi Spectral-Galerkin Method for Nonlinear Volterra Integral Equations with Weakly Singular Kernels
Jie Shen Jie ShenSchool of Mathematical Science, Xiamen University, Xiamen 361005, P. R. ChinaChangtao ShengSchool of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing, Xiamen University, Xiamen 361005, Fujian, P. R. ChinaZhongqing WangSchool of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China
2015en
ABI
Аннотация
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.
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