Numerical Computation for Backward Time-Fractional Di usion Problem
Based on kernel-based approximation technique, we devise in this paper an efficient and accurate numerical scheme for solving a backward problem of time-fractional diffiusion equation(BTFDE). The kernels used in the approximation are the fundamental solutions of the BTFDE which can be expressed in terms of the M-Wright functions. Since each MWright function is a series of complex integrals, we combine the use of the standard Tikhonov regularization technique with an optimal choice for the regularization parameter to obtain a stable and accurate solution from solving the resultant highly ill-conditioned system of linear equations. Numerical results in both 1D and 2D are presented to demonstrate the efficiency of the proposed method.
backward time-fractional diffusion equation kernel-based approximation fundamental solutions Tikhonov regularization.
Y.C. Hon F.F. Dou
Department of Mathematics, City University of Hong Kong, HongKong SAR, China Corresponding author. School of Mathematical Science, University of Electronic Science and Technolog
国际会议
The Fifth Symposium on Fractional Differentiation and Its Applications(第五届国际自动控制联合会分数阶导数及其应用会议)
南京
英文
1-7
2012-05-14（万方平台首次上网日期，不代表论文的发表时间）