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Legendre-collocation method for nonlinear Volterra integral equations of the second kinds
Last modified: 2014-07-15
Abstract
In this paper, we propose an efficient numerical method for Volterra-type nonlinear integral equations, based on Legendre-Gauss-Radau interpolation, which is easy to be implemented and possesses the spectral accuracy. The convergence rate of the
approach is verified rigorously. We also develop a multi-step version of this approach. Numerical results coincide well with the theoretical analysis and demonstrate the effectiveness of these approaches.
approach is verified rigorously. We also develop a multi-step version of this approach. Numerical results coincide well with the theoretical analysis and demonstrate the effectiveness of these approaches.
Keywords
numerical method,error estimation
References
T. Tang, X. Xu and J. Cheng, On spectral methods for Volterra integral equations and the convergence analysis, J. Comput.
Math., 26(6)(2008), pp. 825--837.
Z. Q. Wang and B. Y. Guo, Legendre-Gauss-Radau collocation method for solving initial value problems of first order odinary differential equations, J. Sci. Comput., 52(2012), pp. 226--255.
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