Inverse problem of restoring the right-hand side of the time-fractional diffusion equation
Open Access
- 1 January 2024
- conference paper
- Published by AIP Publishing in AIP Conference Proceedings
- Vol. 3085 (1)
Abstract
The paper considers the parallel algorithm for solving the inverse problem of identifying the space-dependent right-hand part of a time-fractional diffusion equation. After discretization and approximation, the initial boundary problem is reduced to solving the systems of linear algebraic equations. For solving the inverse problem, the iterative conjugate gradient method is used. It requires solving the auxilliary initial boundary problem at each iterative step. On the basis of the parallel sweep method, a parallel algorithm is implemented for multicore processors. Numerical experiments were performed.Keywords
This publication has 11 references indexed in Scilit:
- Identification of stationary source in the anomalous diffusion equationInverse Problems in Science and Engineering, 2021
- Construction of an Explicit Solution of a Time-Fractional Multidimensional Differential EquationMathematics, 2021
- On Stability of the Solution of Multidimensional Inverse Problem for the Schrödinger EquationMathematical Modelling of Natural Phenomena, 2017
- A parallel matrix sweep algorithm for solving linear systems with block-fivediagonal matricesAIP Conference Proceedings, 2015
- Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle trackingPhysical Chemistry Chemical Physics, 2014
- Science metrics on fractional calculus development since 1966Fractional Calculus and Applied Analysis, 2013
- A finite difference method for fractional partial differential equationApplied Mathematics and Computation, 2009
- Numerical Methods for Solving Inverse Problems of Mathematical Physics2007
- Iterative Methods for Sparse Linear Systems2003
- Fractional Derivatives and Integrals1999