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.
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| Main Authors: | , , |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Sociedade Brasileira de Matemática Aplicada e Computacional
2020
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| Online Access: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512020000300521 |
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| Summary: | 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. |
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