Numerical Analysis of the Chebyshev Collocation Method for Functional Volterra Integral Equations
Keyword(s):
L2 Norm
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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.
2017 ◽
Vol 351
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pp. 376-391
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Keyword(s):
2008 ◽
Vol 27
(3)
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pp. 495-507
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1993 ◽
Vol 106
(2)
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pp. 234-257
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2017 ◽
Vol 315
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pp. 424-444
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2018 ◽
Vol 32
(10)
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pp. 4601-4612
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2004 ◽
Vol 40
(2)
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pp. 1021-1024
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2013 ◽
Vol 37
(12)
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pp. 1567-1575
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