Name
Abstract | ||
|---|---|---|
In this study we propose an efficient Kansa-type method of fundamental solutions (MFS-K) for the numerical solution of time-fractional inverse diffusion problems. By approximating the time-fractional derivative through a finite difference scheme, the time-fractional inverse diffusion problem is transformed into a sequence of Cauchy problems associated with inhomogeneous elliptic-type equations, which can be conveniently solved using the MFS-K. Since the matrix arising from the MFS-K discretization is highly ill-conditioned, a regularized solution is obtained by employing the Tikhonov regularization method, while the choice of the regularization parameter is based on the generalized cross-validation criterion. Numerical results are presented for several examples with smooth and piecewise smooth boundaries. The stability of the method with respect to the noise in the data is investigated. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1016/j.camwa.2014.02.008 | Computers & Mathematics with Applications |
Keywords | Field | DocType |
Method of fundamental solutions,Fractional diffusion equation,Inverse problems,Regularization | Tikhonov regularization,Discretization,Inverse,Mathematical optimization,Mathematical analysis,Generalized inverse,Regularization (mathematics),Method of fundamental solutions,Inverse problem,Piecewise,Mathematics | Journal |
Volume | Issue | ISSN |
67 | 8 | 0898-1221 |
Citations | PageRank | References |
1 | 0.37 | 10 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Liang Yan | 1 | 13 | 3.55 |
| Fenglian Yang | 2 | 27 | 3.83 |