Implicit difference approximation for the time fractional diffusion equation
By Pinghui Zhuang, Fawang Liu. 2006
259 citations recorded by the source corpus.
Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/7999055b134d4a95532a0da80bf45be4d299f36d
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In Applied Mathematics
In Modeling and Simulation
In Numerical Analysis
Citations in the corpus
- New Solution and Analytical Techniques of the Implicit Numerical Method for the Anomalous Subdiffusion Equation (2008, methodology): “Zhuang and Liu [22] analyzed an implicit difference approximation for the time fractional diffusion equation, and the stability and convergence of the method were also discussed.”
- A Fourier method for the fractional diffusion equation describing sub-diffusion (2007, methodology): “Some numerical methods for solving the space or time, or time-space fractional partial differential equations have been proposed [15],[16],[17], [18], [19], [20], [21], [22], [23], [24].”
- Analytical solution for the time-fractional telegraph equation by the method of separating variables (2008, background): “[3] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, USA, 1993.”
- A modified quasi-boundary value method for an inverse source problem of the time-fractional diffusion equation (2014, background): “, initial value problem and initial boundary value problems for the time fractional diffusion equation have been studied extensively in recent years, for instance, on maximum principle [17], on some uniqueness and existence results [16,33], on numerical solutions by finite element methods [11,13] an”
- Numerical approximation of Lévy-Feller diffusion equation and its probability interpretation (2007, background): “Zhuang and Liu [37] analyzed an implicit difference approximation for the time fractional diffusion equation, and discussed the stability and convergence of the method.”
- An inverse time-dependent source problem for a time-fractional diffusion equation (2016, unknown): “initial value problems and initial boundary value problems for time-fractional diffusion equations, have attracted much more attention in recent years, for instance, in regard to the maximum principle [15], some uniqueness and existence results [15, 28], numerical solutions by finite element methods”