Numerical Analysis of the Chebyshev Collocation Method for Functional Volterra Integral Equations

J. S. Azevedo, S. M. Afonso, M. P. G. Silva

Abstract


The collocation method based on Chebyshev basis functions, coupled Picard iterative process, is proposed to solve a functional Volterra integral equation of the second kind. Using the Banach Fixed Point Theorem, we prove theorems on the existence and uniqueness solutions in the L2-norm. We also provide the convergence and stability analysis of the proposed method, which indicates that the numerical errors in the L2-norm decay exponentially, provided that the kernel function is sufficiently smooth. Numerical results are presented and they confirm the theoretical prediction of the exponential rate of convergence.


Keywords


Functional Volterra Integral Equation Collocation Method; Picard Iteration

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DOI: https://doi.org/10.5540/tema.2020.021.03.521

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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

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