The Rational Spectral Method Combined with the Laplace Transform for Solving the Robin Time-Fractional Equation
In this paper, the rational spectral method combined with the Laplace transform is proposed for solving Robin time-fractional partial differential equations. First, a time-fractional partial differential equation is transformed into an ordinary differential equation with frequency domain components...
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| Published in | Advances in Mathematical Physics Vol. 2020; no. 2020; pp. 1 - 7 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cairo, Egypt
Hindawi Publishing Corporation
2020
Hindawi John Wiley & Sons, Inc Wiley |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1687-9120 1687-9139 |
| DOI | 10.1155/2020/9865682 |
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| Abstract | In this paper, the rational spectral method combined with the Laplace transform is proposed for solving Robin time-fractional partial differential equations. First, a time-fractional partial differential equation is transformed into an ordinary differential equation with frequency domain components by the Laplace transform. Then, the spatial derivatives are discretized by the rational spectral method, the linear equation with the parameter s is solved, and the approximation Ux,s is obtained. The approximate solution at any given time, which is the numerical inverse Laplace transform, is obtained by the modified Talbot algorithm. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method. |
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| AbstractList | In this paper, the rational spectral method combined with the Laplace transform is proposed for solving Robin time-fractional partial differential equations. First, a time-fractional partial differential equation is transformed into an ordinary differential equation with frequency domain components by the Laplace transform. Then, the spatial derivatives are discretized by the rational spectral method, the linear equation with the parameter
s
is solved, and the approximation
U
x
,
s
is obtained. The approximate solution at any given time, which is the numerical inverse Laplace transform, is obtained by the modified Talbot algorithm. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method. In this paper, the rational spectral method combined with the Laplace transform is proposed for solving Robin time-fractional partial differential equations. First, a time-fractional partial differential equation is transformed into an ordinary differential equation with frequency domain components by the Laplace transform. Then, the spatial derivatives are discretized by the rational spectral method, the linear equation with the parameter s is solved, and the approximation Ux,s is obtained. The approximate solution at any given time, which is the numerical inverse Laplace transform, is obtained by the modified Talbot algorithm. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method. In this paper, the rational spectral method combined with the Laplace transform is proposed for solving Robin time-fractional partial differential equations. First, a time-fractional partial differential equation is transformed into an ordinary differential equation with frequency domain components by the Laplace transform. Then, the spatial derivatives are discretized by the rational spectral method, the linear equation with the parameter s is solved, and the approximation U(x, s) is obtained. The approximate solution at any given time, which is the numerical inverse Laplace transform, is obtained by the modified Talbot algorithm. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method. |
| Audience | Academic |
| Author | Yang, Lufeng |
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| Cites_doi | 10.1016/j.jcp.2007.02.001 10.1093/imamat/23.1.97 10.1016/j.amc.2006.08.163 10.1029/2000WR900031 10.1002/num.22046 10.1002/mma.5497 10.1186/s13662-017-1200-8 10.1108/HFF-07-2016-0278 10.1137/S0036144502417715 10.1016/S0898-1221(02)00183-9 10.1137/050625837 10.1016/0893-9659(96)00089-4 10.1137/030602666 10.3846/13926292.2013.783884 |
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| Copyright | Copyright © 2020 Lufeng Yang. COPYRIGHT 2020 John Wiley & Sons, Inc. Copyright © 2020 Lufeng Yang. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. http://creativecommons.org/licenses/by/4.0 |
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| SubjectTerms | Algorithms Analysis Boundary conditions Calculus Differential equations Laplace transforms Linear equations Mathematical functions Methods Navier-Stokes equations Numerical analysis Ordinary differential equations Partial differential equations Spectra Spectral methods |
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| Title | The Rational Spectral Method Combined with the Laplace Transform for Solving the Robin Time-Fractional Equation |
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