An Efficient Alternating Segment Parallel Difference Method for the Time Fractional Telegraph Equation
The fractional telegraph equation is a kind of important evolution equation, which has an important application in signal analysis such as transmission and propagation of electrical signals. However, it is difficult to obtain the corresponding analytical solution, so it is of great practical value t...
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/6897815 |
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| author | Lifei Wu Xiaozhong Yang |
| author_facet | Lifei Wu Xiaozhong Yang |
| author_sort | Lifei Wu |
| collection | DOAJ |
| description | The fractional telegraph equation is a kind of important evolution equation, which has an important application in signal analysis such as transmission and propagation of electrical signals. However, it is difficult to obtain the corresponding analytical solution, so it is of great practical value to study the numerical solution. In this paper, the alternating segment pure explicit-implicit (PASE-I) and implicit-explicit (PASI-E) parallel difference schemes are constructed for time fractional telegraph equation. Based on the alternating segment technology, the PASE-I and PASI-E schemes are constructed of the classic explicit scheme and implicit scheme. It can be concluded that the schemes are unconditionally stable and convergent by theoretical analysis. The convergence order of the PASE-I and PASI-E methods is second order in spatial direction and 3-α order in temporal direction. The numerical results are in agreement with the theoretical analysis, which shows that the PASE-I and PASI-E schemes are superior to the classical implicit schemes in both accuracy and efficiency. This implies that the parallel difference schemes are efficient for solving the time fractional telegraph equation. |
| format | Article |
| id | doaj-art-1e964f0696984f92a29066799f551a1a |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
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| series | Advances in Mathematical Physics |
| spelling | doaj-art-1e964f0696984f92a29066799f551a1a2025-02-03T01:05:12ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/68978156897815An Efficient Alternating Segment Parallel Difference Method for the Time Fractional Telegraph EquationLifei Wu0Xiaozhong Yang1School of Mathematics and Physics, North China Electric Power University, Beijing 102206, ChinaSchool of Mathematics and Physics, North China Electric Power University, Beijing 102206, ChinaThe fractional telegraph equation is a kind of important evolution equation, which has an important application in signal analysis such as transmission and propagation of electrical signals. However, it is difficult to obtain the corresponding analytical solution, so it is of great practical value to study the numerical solution. In this paper, the alternating segment pure explicit-implicit (PASE-I) and implicit-explicit (PASI-E) parallel difference schemes are constructed for time fractional telegraph equation. Based on the alternating segment technology, the PASE-I and PASI-E schemes are constructed of the classic explicit scheme and implicit scheme. It can be concluded that the schemes are unconditionally stable and convergent by theoretical analysis. The convergence order of the PASE-I and PASI-E methods is second order in spatial direction and 3-α order in temporal direction. The numerical results are in agreement with the theoretical analysis, which shows that the PASE-I and PASI-E schemes are superior to the classical implicit schemes in both accuracy and efficiency. This implies that the parallel difference schemes are efficient for solving the time fractional telegraph equation.http://dx.doi.org/10.1155/2020/6897815 |
| spellingShingle | Lifei Wu Xiaozhong Yang An Efficient Alternating Segment Parallel Difference Method for the Time Fractional Telegraph Equation Advances in Mathematical Physics |
| title | An Efficient Alternating Segment Parallel Difference Method for the Time Fractional Telegraph Equation |
| title_full | An Efficient Alternating Segment Parallel Difference Method for the Time Fractional Telegraph Equation |
| title_fullStr | An Efficient Alternating Segment Parallel Difference Method for the Time Fractional Telegraph Equation |
| title_full_unstemmed | An Efficient Alternating Segment Parallel Difference Method for the Time Fractional Telegraph Equation |
| title_short | An Efficient Alternating Segment Parallel Difference Method for the Time Fractional Telegraph Equation |
| title_sort | efficient alternating segment parallel difference method for the time fractional telegraph equation |
| url | http://dx.doi.org/10.1155/2020/6897815 |
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