On numerical approximation for fractional order diffusion equation

In this study, numerical solution methods depending on the number of points of two-dimensional, time fractional order diffusion equation with locally one dimensional -LOD method have been developed. By applying the LOD method the equation is made discrete using appropriate finite difference approaches instead of the derivatives. While using the definition of fractional derivative in the sense of Caputo, which is frequently used in the literatur for the derivative in time dimension, the appropriate central finite difference definition is used instead of the integer derivative. Finite difference definitions are handled to increase the number of points. The numerical results are obtained by solving the equation systems obtained for each case. The results are analyzed with tables and graphs and the aprroaches made are found to have sufficient precision. The error analysis and stability of the method is examined for each case .