In this paper, a Jacobi spectral Galerkin method is developed for nonlinear Volterra integral equations (VIEs) of the second kind. The spectral rate of convergence for the proposed method is established in the -norm and the weighted L2-norm. Global superconvergence properties are discussed by iterated Galerkin methods. Numerical results are presented to demonstrate the effectiveness of the proposed method.
Jacobi Spectral Galerkin and Iterated Methods for Nonlinear Volterra Integral Equation
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 23, 2015; final manuscript received April 11, 2016; published online May 24, 2016. Assoc. Editor: Zdravko Terze.
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Yang, Y., and Chen, Y. (May 24, 2016). "Jacobi Spectral Galerkin and Iterated Methods for Nonlinear Volterra Integral Equation." ASME. J. Comput. Nonlinear Dynam. July 2016; 11(4): 041027. https://doi.org/10.1115/1.4033439
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