Name
Title | ||
|---|---|---|
A new regularization method for a Cauchy problem of the time fractional diffusion equation |
Abstract | ||
|---|---|---|
In this paper, we consider a Cauchy problem of the time fractional diffusion equation (TFDE). Such problem is obtained from the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative of order 驴 (0驴驴驴驴驴1). We show that the Cauchy problem of TFDE is severely ill-posed and further apply a new regularization method to solve it based on the solution given by the Fourier method. Convergence estimates in the interior and on the boundary of solution domain are obtained respectively under different a-priori bound assumptions for the exact solution and suitable choices of regularization parameters. Finally, numerical examples are given to show that the proposed numerical method is effective. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1007/s10444-011-9206-3 | Adv. Comput. Math. |
Keywords | Field | DocType |
Regularization method,Cauchy problem,Time fractional diffusion equation,Caputo fractional derivative,Fourier transform,Convergence estimate,Solute concentration,35R11,35R25,35R30,65J20,65J22 | Cauchy problem,Mathematical optimization,Mathematical analysis,Time derivative,Fourier transform,Regularization (mathematics),Fractional calculus,Initial value problem,Numerical analysis,Mathematics,Diffusion equation | Journal |
Volume | Issue | ISSN |
36 | 2 | 1019-7168 |
Citations | PageRank | References |
7 | 0.70 | 6 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| G. H. Zheng | 1 | 23 | 1.98 |
| T. Wei | 2 | 87 | 18.96 |