Convergence Analysis of the Legendre Spectral Collocation Methods for Second Order Volterra Integro-Differential Equations |
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| Authors: | Yunxia Wei Yanping Chen |
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| Institution: | 1. School of Mathematics and Computational Science, Sun Yat-sen University,Guangzhou 510275, China
2. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China |
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| Abstract: | A class of numerical methods is developed for second order Volterra integrodifferential equations by using a Legendre spectral approach.We provide a rigorous error analysis for the proposed methods,which shows that the numerical errors decay exponentially in the L∞-norm and L2-norm.Numerical examples illustrate the convergence and effectiveness of the numerical methods. |
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| Keywords: | Second order Volterra integro-differential equations Gauss quadrature tormula Legendre-collocation methods convergence analysis |
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