Journals Information
Mathematics and Statistics Vol. 8(2A), pp. 52 - 57
DOI: 10.13189/ms.2020.081309
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Fourth-order Compact Iterative Scheme for the Two-dimensional Time Fractional Sub-diffusion Equations
Muhammad Asim Khan *, Norhashidah Hj. Mohd Ali
School of Mathematical Sciences, Universiti Sains Malaysia, Malaysia
ABSTRACT
The fractional diffusion equation is an important mathematical model for describing phenomena of anomalous diffusion in transport processes. A high-order compact iterative scheme is formulated in solving the two-dimensional time fractional sub-diffusion equation. The spatial derivative is evaluated using Crank-Nicolson scheme with a fourth-order compact approximation and the Caputo derivative is used for the time fractional derivative to obtain a discrete implicit scheme. The order of convergence for the proposed method will be shown to be of . Numerical examples are provided to verify the high-order accuracy solutions of the proposed scheme.
KEYWORDS
High-order Compact Scheme, Crank-nicolson, Finite Difference, Two-dimensional Time Fractional Sub-diffusion
Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Muhammad Asim Khan , Norhashidah Hj. Mohd Ali , "Fourth-order Compact Iterative Scheme for the Two-dimensional Time Fractional Sub-diffusion Equations," Mathematics and Statistics, Vol. 8, No. 2A, pp. 52 - 57, 2020. DOI: 10.13189/ms.2020.081309.
(b). APA Format:
Muhammad Asim Khan , Norhashidah Hj. Mohd Ali (2020). Fourth-order Compact Iterative Scheme for the Two-dimensional Time Fractional Sub-diffusion Equations. Mathematics and Statistics, 8(2A), 52 - 57. DOI: 10.13189/ms.2020.081309.