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

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.

Keywords:
functional Volterra integral equation collocation method; Picard iteration