KMS Of Academy of mathematics and systems sciences, CAS
| Convolution Quadrature Methods for Time-Space Fractional Nonlinear Diffusion-Wave Equations | |
Huang, Jianfei1; Arshad, Sadia2; Jiao, Yandong3; Tang, Yifa4,5
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| 2019-08-01 | |
| Source Publication | EAST ASIAN JOURNAL ON APPLIED MATHEMATICS
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| ISSN | 2079-7362 |
| Volume | 9Issue:3Pages:538-557 |
| Abstract | Two second-order convolution quadrature methods for fractional nonlinear diffusion-wave equations with Caputo derivative in time and Riesz derivative in space are constructed. To improve the numerical stability, the fractional diffusion-wave equations are firstly transformed into equivalent partial integro-differential equations. Then, a second-order convolution quadrature is applied to approximate the Riemann-Liouville integral. This deduced convolution quadrature method can handle solutions with low regularity in time. In addition, another second-order convolution quadrature method based on a new second-order approximation for discretising the Riemann-Liouville integral at time t(k-1/2) is constructed. This method reduces computational complexity if Crank-Nicolson technique is used. The stability and convergence of the methods are rigorously proved. Numerical experiments support the theoretical results. |
| Keyword | Fractional diffusion-wave equation nonlinear source convolution quadrature generating function stability and convergence |
| DOI | 10.4208/eajam.230718.131018 |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11701502] ; National Natural Science Foundation of China[11771438] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000470088100008 |
| Publisher | GLOBAL SCIENCE PRESS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/34852 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Jiao, Yandong |
| Affiliation | 1.Yangzhou Univ, Coll Math Sci, Yangzhou 225002, Jiangsu, Peoples R China 2.COMSATS Inst Informat Technol, Lahore, Pakistan 3.Hebei Univ Technol, Sch Sci, Tianjin 300401, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 5.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| Recommended Citation GB/T 7714 | Huang, Jianfei,Arshad, Sadia,Jiao, Yandong,et al. Convolution Quadrature Methods for Time-Space Fractional Nonlinear Diffusion-Wave Equations[J]. EAST ASIAN JOURNAL ON APPLIED MATHEMATICS,2019,9(3):538-557. |
| APA | Huang, Jianfei,Arshad, Sadia,Jiao, Yandong,&Tang, Yifa.(2019).Convolution Quadrature Methods for Time-Space Fractional Nonlinear Diffusion-Wave Equations.EAST ASIAN JOURNAL ON APPLIED MATHEMATICS,9(3),538-557. |
| MLA | Huang, Jianfei,et al."Convolution Quadrature Methods for Time-Space Fractional Nonlinear Diffusion-Wave Equations".EAST ASIAN JOURNAL ON APPLIED MATHEMATICS 9.3(2019):538-557. |
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