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

• Autor(a) principal: Azevedo, J. S.
• Data de Publicação: 2020
• Outros Autores: Afonso, S. M. [UNESP], Da Silva, M. P. G.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.5540/tema.2020.021.03.0521; http://hdl.handle.net/11449/212217
• topic: functional Volterra integral equation collocation method; Picard iteration; método de colocação de equação integral funcional de Volterra; iteração de Picard

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 L 2-norm. We also provide the convergence and stability analysis of the proposed method, which indicates that the numerical errors in the L 2-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.