The error analysis of Crank-Nicolson-type difference scheme for fractional subdiffusion equation with spatially variable coefficient
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- 作者：Pu Zhang ; Hai Pu
- 关键词：fractional subdiffusion equation ; variable coefficient ; finite difference ; stability ; convergence
- 刊名：Boundary Value Problems
- 出版年：2017
- 出版时间：December 2017
- 年：2017
- 卷：2017
- 期：1
- 全文大小：1639KB
- 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
- 出版者：Springer International Publishing
- ISSN：1687-2770
- 卷排序：2017
文摘
A Crank-Nicolson-type difference scheme is presented for the spatial variable coefficient subdiffusion equation with Riemann-Liouville fractional derivative. The truncation errors in temporal and spatial directions are analyzed rigorously. At each time level, it results in a linear system in which the coefficient matrix is tridiagonal and strictly diagonally dominant, so it can be solved by the Thomas algorithm. The unconditional stability and convergence of the scheme are proved in the discrete \(L_{2}\) norm by the energy method. The convergence order is \(\min \{2-\frac{\alpha}{2}, 1+\alpha \}\) in the temporal direction and two in the spatial one. Finally, numerical examples are presented to verify the efficiency of our method.