KMS Of Academy of mathematics and systems sciences, CAS
| A superlinear convergence scheme for the multi-term and distribution-order fractional wave equation with initial singularity | |
| Huang, Jianfei1; Zhang, Jingna1; Arshad, Sadia2; Tang, Yifa3,4 | |
| 2021-01-22 | |
| Source Publication | NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
 |
| ISSN | 0749-159X |
| Pages | 16 |
| Abstract | In this paper, a superlinear convergence scheme for the multi-term and distribution-order fractional wave equation with initial singularity is proposed. The initial singularity of the solution of the multi-term time fractional partial differential equation often generate a singular source, it increases the difficulty to numerically solve the equation. Thus, after discretizing the spatial distribution-order derivative by the midpoint quadrature, an integral transformation is applied to deal with the temporal direction for obtaining a temporal superlinear convergence scheme based on the uniform mesh. Then, the fully discrete scheme is constructed by using Crank-Nicolson technique and L1 approximation in time, and fractional centered difference approximation in space. The convergence and stability of the proposed scheme are rigorously analyzed. Finally, numerical experiments are presented to support the theoretical results of our scheme. |
| Keyword | distribution-order derivative fractional wave equations initial singularity multi-term fractional derivatives superlinear convergence |
| DOI | 10.1002/num.22773 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11701502] ; National Natural Science Foundation of China[11871065] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000609934200001 |
| Publisher | WILEY |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58068 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Huang, Jianfei |
| Affiliation | 1.Yangzhou Univ, Coll Math Sci, Yangzhou 225002, Jiangsu, Peoples R China 2.COMSATS Univ Islamabad, Lahore Campus, Lahore, Pakistan 3.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China |
| Recommended Citation GB/T 7714 | Huang, Jianfei,Zhang, Jingna,Arshad, Sadia,et al. A superlinear convergence scheme for the multi-term and distribution-order fractional wave equation with initial singularity[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,2021:16. |
| APA | Huang, Jianfei,Zhang, Jingna,Arshad, Sadia,&Tang, Yifa.(2021).A superlinear convergence scheme for the multi-term and distribution-order fractional wave equation with initial singularity.NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,16. |
| MLA | Huang, Jianfei,et al."A superlinear convergence scheme for the multi-term and distribution-order fractional wave equation with initial singularity".NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS (2021):16. |
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