کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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512699 | 866422 | 2012 | 9 صفحه PDF | دانلود رایگان |
We investigate in this paper a Cauchy problem for the time-fractional diffusion equation (TFDE). Based on the idea of kernel-based approximation, we construct an efficient numerical scheme for obtaining the solution of a Cauchy problem of TFDE. The use of M-Wright functions as the kernel functions for the approximation space allows us to express the solution in terms of M-Wright functions, whose numerical evaluation can be accurately achieved by applying the inverse Laplace transform technique. To handle the ill-posedness of the resultant coefficient matrix due to the noisy Cauchy data, we adapt the standard Tikhonov regularization technique with the L-curve method for obtaining the optimal regularization parameter to give a stable numerical reconstruction of the solution. Numerical results indicate the efficiency and effectiveness of the proposed scheme.
Journal: Engineering Analysis with Boundary Elements - Volume 36, Issue 9, September 2012, Pages 1344–1352