Name
Title | ||
|---|---|---|
Numerical Approximation of a Time Dependent, Nonlinear, Space-Fractional Diffusion Equation |
Abstract | ||
|---|---|---|
In this article we analyze a fully discrete numerical approximation to a time dependent fractional order diffusion equation which contains a nonlocal quadratic nonlinearity. The analysis is performed for a general fractional order diffusion operator. The nonlinear term studied is a product of the unknown function and a convolution operator of order 0. Convergence of the approximation and a priori error estimates are given. Numerical computations are included, which confirm the theoretical predictions. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1137/050642757 | SIAM J. Numerical Analysis |
Keywords | Field | DocType |
diffusion equation,convolution operator,error estimate,anomalous diffusion,numerical approximation,finite element approximation,nonlinear term,discrete numerical approximation,theoretical prediction,space-fractional diffusion equation,nonlocal quadratic nonlinearity,time dependent,time dependent fractional order,nonlinear parabolic equation,general fractional order diffusion,numerical computation | Order of accuracy,Mathematical optimization,Nonlinear system,Mathematical analysis,Convolution,Quadratic equation,Numerical analysis,Mathematics,Diffusion equation,Anomalous diffusion,Approximation error | Journal |
Volume | Issue | ISSN |
45 | 2 | 0036-1429 |
Citations | PageRank | References |
67 | 6.02 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Vincent J. Ervin | 1 | 118 | 15.66 |
| Norbert Heuer | 2 | 263 | 39.70 |
| John Paul Roop | 3 | 94 | 11.20 |