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., DA SILVA,M. P. G.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512020000300521
• topic: 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 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.