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- Title
The Implicit Numerical Method for the Radial Anomalous Subdiffusion Equation.
- Authors
Błasik, Marek
- 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 the 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 via the two methods.
- Subjects
CAPUTO fractional derivatives; CRANK-nicolson method; EQUATIONS; FRACTIONAL calculus
- Publication
Symmetry (20738994), 2023, Vol 15, Issue 9, p1642
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym15091642