A high-order and unconditionally stable scheme for the modified anomalous fractional sub-diffusion equation with a nonlinear source term

作者：Mohebbi Akbar; Abbaszadeh Mostafa; Dehghan Mehdi^*

来源：Journal of Computational Physics, 2013, 240: 36-48.

DOI：10.1016/j.jcp.2012.11.052

• Modified anomalous fractional sub-diffusion equation
• Compact finite difference
• Fourier analysis
• Solvability
• Unconditional stability convergence

The aim of this paper is to study the high order difference scheme for the solution of modified anomalous fractional sub-diffusion equation. The time fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald-Letnikov discretization of the Riemann-Liouville derivative to obtain a fully discrete implicit scheme. We analyze the solvability, stability and convergence of the proposed scheme using the Fourier method. The convergence order of method is O(tau + h(4)). Numerical examples demonstrate the theoretical results and high accuracy of the proposed scheme.

• 出版日期2013-5-1