Numerical Analysis of the Chebyshev Collocation Method for Functional Volterra Integral Equations
DOI:
https://doi.org/10.5540/tema.2020.021.03.521Keywords:
Functional Volterra Integral Equation Collocation Method, Picard IterationAbstract
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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