A Compact Difference Scheme for Fractional Sub-diffusion Equations with the Spatially Variable Coefficient Under Neumann Boundary Conditions

• Published in: Journal of scientific computing Vol. 66; no. 2; pp. 725 - 739
• Main Authors: Vong, Seakweng, Lyu, Pin, Wang, Zhibo
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2016; Springer Nature B.V
• Subjects: Accuracy; Algorithms; Approximation; Boundary conditions; Coefficients; Computational Mathematics and Numerical Analysis; Convergence; Decomposition; Energy; Energy methods; Finite difference method; Fourier transforms; Mathematical analysis; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical models; Mathematics; Mathematics and Statistics; Porous materials; Stability; Theoretical; Energy method; Variable coefficient; Compact difference scheme; Fractional sub-diffusion equation; Neumann boundary conditions
• ISSN: 0885-7474; 1573-7691
• DOI: 10.1007/s10915-015-0040-5

In this paper, a compact finite difference scheme with global convergence order O ( τ 2 - α + h 4 ) is derived for fractional sub-diffusion equations with the spatially variable coefficient subject to Neumann boundary conditions. The difficulty caused by the variable coefficient and the Neumann boundary conditions is overcome by subtle decomposition of the coefficient matrices. The stability and convergence of the proposed scheme are studied using its matrix form by the energy method. The theoretical results are supported by numerical experiments.