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The Implicit Numerical Method for the Radial Anomalous Subdiffusion Equation
Version 1
: Received: 31 July 2023 / Approved: 31 July 2023 / Online: 1 August 2023 (03:41:51 CEST)
A peer-reviewed article of this Preprint also exists.
Błasik, M. The Implicit Numerical Method for the Radial Anomalous Subdiffusion Equation. Symmetry 2023, 15, 1642. Błasik, M. The Implicit Numerical Method for the Radial Anomalous Subdiffusion Equation. Symmetry 2023, 15, 1642.
Abstract
This paper presents a numerical method for solving a two-dimensional subdiffusion equation with a Caputo fractional derivative. The problem considered assumes symmetry in both the equation’s solution domain and the boundary conditions, allowing for a reduction of the two-dimensional equation to a one-dimensional one. The proposed method is an extension of the fractional Crank-Nicolson method, based on the discretization of the equivalent integral-differential equation. To validate the method, the obtained results were compared with a solution obtained through Laplace transform. The analytical solution in the image of the Laplace transform was inverted using the Gaver-Wynn-Rho algorithm implemented in the specialized mathematical computing environment, Wolfram Mathematica. The results clearly show the mutual convergence of the solutions obtained by the two methods.
Keywords
fractional derivatives and integrals; integro-differential equations; numerical methods; anomalous diffusion
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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