A Newton Linearized Crank-Nicolson Method for the Nonlinear Space Fractional Sobolev Equation
| Autor: | Xiaocheng Yang, Wahidullah Niazi, Yifan Qin, Yunzhu Ren, Yinghong Xu |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Discretization
Article Subject Numerical analysis Finite difference method 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics Sobolev space Nonlinear system Norm (mathematics) QA1-939 Crank–Nicolson method Applied mathematics Uniqueness 0101 mathematics Analysis Mathematics |
| Zdroj: | Journal of Function Spaces, Vol 2021 (2021) |
| ISSN: | 2314-8896 |
| DOI: | 10.1155/2021/9979791 |
| Popis: | In this paper, one class of finite difference scheme is proposed to solve nonlinear space fractional Sobolev equation based on the Crank-Nicolson (CN) method. Firstly, a fractional centered finite difference method in space and the CN method in time are utilized to discretize the original equation. Next, the existence, uniqueness, stability, and convergence of the numerical method are analyzed at length, and the convergence orders are proved to be O τ 2 + h 2 in the sense of l 2 -norm, H α / 2 -norm, and l ∞ -norm. Finally, the extensive numerical examples are carried out to verify our theoretical results and show the effectiveness of our algorithm in simulating spatial fractional Sobolev equation. |
| Databáze: | OpenAIRE |
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