Journal
APPLIED NUMERICAL MATHEMATICS
Volume 167, Issue -, Pages 218-236Publisher
ELSEVIER
DOI: 10.1016/j.apnum.2021.05.006
Keywords
Volterra integral equation; Weakly singular kernel; Multi-domain spectral collocation; Nonpolynomial collocation; Graded mesh; Error analysis
Categories
Funding
- National Natural Science Foundation of China [12011530058, 11771163]
- RFBR [20-51-53007]
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This paper introduces a multi-domain Muntz-polynomial spectral collocation method with graded meshes for solving second kind Volterra integral equations with a weakly singular kernel, particularly suitable for problems with non-integer exponent factors in the solutions. A rigorous error analysis of hp-version in the L-infinity- and weighted L-2-norms is carried out, and several numerical examples are presented to demonstrate the efficiency and accuracy of the method.
In this paper, we introduce a multi-domain Muntz-polynomial spectral collocation method with graded meshes for solving second kind Volterra integral equations with a weakly singular kernel. This method is particularly suitable for problems whose solutions contain non-integer exponent factors. We carry out a rigorous error analysis of hp-version in the L-infinity- and weighted L-2-norms. Several numerical examples are presented to demonstrate the efficiency and accuracy of the method. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.
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