TY - JOUR
T1 - Numerical Solution of the Time-Fractional Sub-Diffusion Equation on an Unbounded Domain in Two-Dimensional Space
AU - Li, Hongwei
AU - Wu, Xiaonan
AU - Zhang, Jiwei
N1 - Funding Information:
H. Li was supported by NSFC under Grant Nos. 11401350 and 11471196, and the China Scholarship Council (No. 201608370010). Part of the work was done when H. Li visited Hong Kong Baptist University. J. Zhang is partially supported by NSFC under Grant Nos. 91430216 and U1530401, and X. Wu was supported by the General Research Fund of Hong Kong under Grant No. HKBU 12302414 32-14-324.
Publisher copyright:
Copyright © Global-Science Press 2017
PY - 2017/8
Y1 - 2017/8
N2 - 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.
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.
KW - Caputo time-fractional derivative
KW - finite difference method
KW - Fractional sub-diffusion equation
KW - local artificial boundary conditions
KW - unbounded domain
UR - https://www.global-sci.org/intro/articles_list/eajam/1388.html
UR - http://www.scopus.com/inward/record.url?scp=85029483119&partnerID=8YFLogxK
U2 - 10.4208/eajam.031116.080317a
DO - 10.4208/eajam.031116.080317a
M3 - Journal article
AN - SCOPUS:85029483119
SN - 2079-7362
VL - 7
SP - 439
EP - 454
JO - East Asian Journal on Applied Mathematics
JF - East Asian Journal on Applied Mathematics
IS - 3
ER -