Abstract
Here, we searched stability and convergence of a difference scheme which is constructed for solving a fractional partial differential equation with Caputo fractional derivative. Stability is proved by matrix method. Numerical experiments are presented. Mathematics Subject Classification: 65N06, 65N12, 65M12
Highlights
There are two fundamental types of fractional heat equations, time fractional heat equations and space fractional heat equations
The Crank-Nicholson method was applied directly to obtain a numerical solution for time fractional advection dispersion equations with Riemann Liouville derivative in [8]
We use a numerical approximation based on the CrankNicholson method for fractional derivatives
Summary
There are two fundamental types of fractional heat equations, time fractional heat equations and space fractional heat equations. Some difference schemes for the space-fractional heat equations are presented in [6][15][16]. The Crank-Nicholson method was applied directly to obtain a numerical solution for time fractional advection dispersion equations with Riemann Liouville derivative in [8]. We use a numerical approximation based on the CrankNicholson method for fractional derivatives. The matrix stability of the method is proved conditionally. We consider the following time fractional heat equation;.
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