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

Authors

  • J. S. Azevedo Universidade Federal da Bahia - UFBA, Instituto de Ciencias, Tecnologia e Inovação Centro, 42802-721, Camaçari-BA, Brazil
  • S. M. Afonso UNESP
  • M. P. G. Silva UFRB

DOI:

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

Keywords:

Functional Volterra Integral Equation Collocation Method, Picard Iteration

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.

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Published

2020-11-27

How to Cite

Azevedo, J. S., Afonso, S. M., & Silva, M. P. G. (2020). Numerical Analysis of the Chebyshev Collocation Method for Functional Volterra Integral Equations. Trends in Computational and Applied Mathematics, 21(3), 521. https://doi.org/10.5540/tema.2020.021.03.521

Issue

Vol. 21 No. 3 (2020)

Section

Original Article

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