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Medientyp:
E-Artikel
Titel:
Numerical Analysis of the Chebyshev Collocation Method for Functional Volterra Integral Equations
Beteiligte:
Azevedo, J. S.;
Afonso, S. M.;
Silva, M. P. G.
Erschienen:
Brazilian Society for Computational and Applied Mathematics (SBMAC), 2020
Erschienen in:
TEMA (São Carlos), 21 (2020) 3, Seite 521
Sprache:
Ohne Angabe
DOI:
10.5540/tema.2020.021.03.521
ISSN:
2179-8451;
1677-1966
Entstehung:
Anmerkungen:
Beschreibung:
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.