The regularization of spectral methods for hyperbolic Volterra integrodifferential equations with fractional power elliptic operator
Abstract: In this study, a numerical approach is presented to solve the linear and nonlinear hyperbolic Volterra integrodifferential equations (HVIDEs). The regularization of a Legendre-collocation spectral method is applied for solving HVIDE of the second kind, with the time and space variables on the basis of Legendre-Gauss-Lobatto and Legendre-Gauss (LG) interpolation points, respectively. Concerning bounded domains, the provided HVIDE relation is transformed into three corresponding relations. Hence, a Legendre-collocation spectral approach is applied for solving this equation, and finally, ill-posed linear and nonlinear systems of algebraic equations are obtained; therefore different regularization methods are used to solve them. For an unbounded domain, a suitable mapping to convert the problem on a bounded domain is used and then apply the same proposed method for the bounded domain. For the two cases, the numerical results confirm the exponential convergence rate. The findings of this study are unprecedented for the regularization of the spectral method for the hyperbolic integrodifferential equation. The result in this work seems to be the first successful for the regularization of spectral method for the hyperbolic integrodifferential equation.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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The regularization of spectral methods for hyperbolic Volterra integrodifferential equations with fractional power elliptic operator ; volume:12 ; number:1 ; year:2023 ; extent:19
Nonlinear engineering ; 12, Heft 1 (2023) (gesamt 19)
- Creator
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Mirzaei G., F.
Rostamy, Davood
- DOI
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10.1515/nleng-2022-0250
- URN
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urn:nbn:de:101:1-2023020913020785640169
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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14.08.2025, 11:03 AM CEST
Data provider
Deutsche Nationalbibliothek. If you have any questions about the object, please contact the data provider.
Associated
- Mirzaei G., F.
- Rostamy, Davood
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