Monotone method for initial value problem for fractional diffusion equation

2006 ◽  
Vol 49 (9) ◽  
pp. 1223-1230 ◽  
Author(s):  
Shuqin Zhang
Keyword(s):  
Diffusion Equation ◽  
Initial Value Problem ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Initial Value ◽  
Monotone Method

Hermite Pseudospectral Method for the Time Fractional Diffusion Equation with Variable Coefficients

2017 ◽  
Vol 18 (5) ◽  
pp. 385-393
Author(s):  
Zeting Liu ◽  
Shujuan Lü
Keyword(s):  
Diffusion Equation ◽  
Pseudospectral Method ◽  
Fractional Diffusion ◽  
Variable Coefficients ◽  
Fractional Diffusion Equation ◽  
Stability And Convergence ◽  
Initial Value ◽  
Fully Discrete ◽  
Time Fractional Diffusion Equation ◽  
Gauss Points

Abstract:We consider the initial value problem of the time fractional diffusion equation on the whole line and the fractional derivative is described in Caputo sense. A fully discrete Hermite pseudospectral approximation scheme is structured basing Hermite-Gauss points in space and finite difference in time. Unconditionally stability and convergence are proved. Numerical experiments are presented and the results conform to our theoretical analysis.

A quasi-boundary regularization method for identifying the initial value of time-fractional diffusion equation on spherically symmetric domain

2019 ◽  
Vol 27 (5) ◽  
pp. 609-621 ◽  
Author(s):  
Fan Yang ◽  
Ni Wang ◽  
Xiao-Xiao Li ◽  
Can-Yun Huang
Keyword(s):  
Diffusion Equation ◽  
Regularization Method ◽  
Regularization Parameter ◽  
A Priori ◽  
Symmetric Domain ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Spherically Symmetric ◽  
Initial Value ◽  
Time Fractional Diffusion Equation

Abstract In this paper, an inverse problem to identify the initial value for high dimension time fractional diffusion equation on spherically symmetric domain is considered. This problem is ill-posed in the sense of Hadamard, so the quasi-boundary regularization method is proposed to solve the problem. The convergence estimates between the regularization solution and the exact solution are presented under the a priori and a posteriori regularization parameter choice rules. Numerical examples are provided to show the effectiveness and stability of the proposed method.

Fractional diffusion equation in half-space with Robin boundary condition

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Jun-Sheng Duan ◽  
Zhong Wang ◽  
Shou-Zhong Fu
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Half Space ◽  
Boundary Value ◽  
Robin Boundary Condition ◽  
Fundamental Solutions ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Initial Value ◽  
Robin Boundary

AbstractThe initial and boundary value problem for the fractional diffusion equation in half-space with the Robin boundary condition is considered. The solution is comprised of two parts: the contribution of the initial value and the contribution of the boundary value, for which the respective fundamental solutions are given. Finally, the solution formula of the considered problem is obtained.

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