Three Landweber iterative methods for solving the initial value problem of time-fractional diffusion-wave equation on spherically symmetric domain

2021 ◽  
pp. 1-51
Author(s):  
Fan Yang ◽  
Qiao-Xi Sun ◽  
Xiao-Xiao Li
Keyword(s):  
Wave Equation ◽  
Iterative Methods ◽  
Initial Value Problem ◽  
Symmetric Domain ◽  
Fractional Diffusion ◽  
Spherically Symmetric ◽  
Initial Value ◽  
Diffusion Wave ◽  
Problem Of Time

Inversion of the Initial Value for a Time-Fractional Diffusion-Wave Equation by Boundary Data

2020 ◽  
Vol 20 (1) ◽  
pp. 109-120 ◽  
Author(s):  
Suzhen Jiang ◽  
Kaifang Liao ◽  
Ting Wei
Keyword(s):  
Inverse Problem ◽  
Wave Equation ◽  
Fractional Diffusion ◽  
Initial Value ◽  
Diffusion Wave ◽  
One Dimensional ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation ◽  
Continuation Technique

AbstractIn this study, we consider an inverse problem of recovering the initial value for a multi-dimensional time-fractional diffusion-wave equation. By using some additional boundary measured data, the uniqueness of the inverse initial value problem is proven by the Laplace transformation and the analytic continuation technique. The inverse problem is formulated to solve a Tikhonov-type optimization problem by using a finite-dimensional approximation. We test four numerical examples in one-dimensional and two-dimensional cases for verifying the effectiveness of the proposed algorithm.

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.

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