Journal
MATHEMATICS
Volume 10, Issue 17, Pages -Publisher
MDPI
DOI: 10.3390/math10173160
Keywords
space-time fractional advection diffusion equation; Riemann-Liouville fractional derivative; Caputo fractional derivative; Crank-Nicolson finite difference scheme; stability; convergence
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This article presents the analytical and numerical solution of a one-dimensional space-time fractional advection diffusion equation. The analytical solution is carried out using the separation of variables method, and the numerical solution is based on constructing the Crank-Nicolson finite difference scheme. The convergence and unconditional stability of the solution are investigated.
In this article, the analytical and numerical solution of a one-dimensional space-time fractional advection diffusion equation is presented. The separation of variables method is used to carry out the analytical solution, the basis of the system eigenfunction and their corresponding eigenvalue for basic equation is determined, and the numerical solution is based on constructing the Crank-Nicolson finite difference scheme of the equivalent partial integro-differential equations. The convergence and unconditional stability of the solution are investigated. Finally, the numerical and analytical experiments are given to verify the theoretical analysis.
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