An Effective Algorithm for Delay Fractional Convection-Diffusion Wave Equation Based on Reversible Exponential Recovery Method
| Autor: | Wahidullah Niazi, Yinghong Xu, Qifeng Zhang, Tingyue Li, Maohua Ran |
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| Rok vydání: | 2019 |
| Předmět: |
General Computer Science
Inverse 010103 numerical & computational mathematics 01 natural sciences Exponential recovery semilinear Exponential stability Gronwall's inequality ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Applied mathematics General Materials Science 0101 mathematics Mathematics convergence General Engineering stability Wave equation Exponential function 010101 applied mathematics variable coefficient Norm (mathematics) ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Computer Science::Programming Languages lcsh:Electrical engineering. Electronics. Nuclear engineering Convection–diffusion equation lcsh:TK1-9971 solvability Numerical stability |
| Zdroj: | IEEE Access, Vol 7, Pp 5554-5563 (2019) |
| ISSN: | 2169-3536 |
| DOI: | 10.1109/access.2018.2889735 |
| Popis: | In this paper, we investigate a linearized finite difference scheme for the variable coefficient semi-linear fractional convection-diffusion wave equation with delay. Based on reversible recovery technique, the original problems are transformed into an equivalent variable coefficient semi-linear fractional delay reaction-diffusion equation. Then, the temporal Caputo derivative is discreted by using $L_{1}$ approximation and the second-order spatial derivative is approximated by the centered finite difference scheme. The numerical solution can be obtained by an inverse exponential recovery method. By introducing a new weighted norm and applying discrete Gronwall inequality, the solvability, unconditionally stability, and convergence in the sense of $L_{2}$ - and $L_{\infty }$ - norms are proved rigorously. Finally, we present a numerical example to verify the effectiveness of our algorithm. |
| Databáze: | OpenAIRE |
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