TY - JOUR T1 - Numerical Solution of the Time-Fractional Sub-Diffusion Equation on an Unbounded Domain in Two-Dimensional Space JO - East Asian Journal on Applied Mathematics VL - 3 SP - 439 EP - 454 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.031116.080317a UR - https://global-sci.org/intro/article_detail/eajam/10758.html KW - Fractional sub-diffusion equation, unbounded domain, local artificial boundary conditions, finite difference method, Caputo time-fractional derivative. AB -

The numerical solution of the time-fractional sub-diffusion equation on an unbounded domain in two-dimensional space is considered, where a circular artificial boundary is introduced to divide the unbounded domain into a bounded computational domain and an unbounded exterior domain. The local artificial boundary conditions for the fractional sub-diffusion equation are designed on the circular artificial boundary by a joint Laplace transform and Fourier series expansion, and some auxiliary variables are introduced to circumvent high-order derivatives in the artificial boundary conditions. The original problem defined on the unbounded domain is thus reduced to an initial boundary value problem on a bounded computational domain. A finite difference and L1 approximation are applied for the space variables and the Caputo time-fractional derivative, respectively. Two numerical examples demonstrate the performance of the proposed method.