Numerical studies for anomalous subdiffusion equations /
Mohamed Adel Hosny
Numerical studies for anomalous subdiffusion equations / دراسات عددية للمعادلات جزئية الانتشار غير المعتادة Mohamed Adel Hosny ; Supervised L. F. Abdelelal , N. H. Sweilam , M. M. Khader - Cairo : Mohamed Adel Hosny , 2014 - 136 P. ; 25cm
Thesis (Ph.D.) - Cairo University - Faculty of Science - Department of Mathematics
This thesis is a contribution on numerical studies for anomalous subdiffusion equations. A class of numerical methods for solving two of the most important anomalous subdiffusion equations which are the fractional cable equation (FCE) of spiny neuronal dendrites and the fractional reaction - subdiffusion equation (FRSE) is presented. This class of methods is very close to the weighted average finite difference method (WAFDM). Theorems with their proofs are presented to study the stability analysis and the truncation error of the proposed method. Also, a numerical method depends on the finite difference method based on Hermite formula is presented to solve two of the anomalous subdiffusion equations which are the fractional reaction - subdiffusion equation and the fractional diffusion - wave equation
Anomalous subdiffusion equations Fractional diffusion Mathematics
Numerical studies for anomalous subdiffusion equations / دراسات عددية للمعادلات جزئية الانتشار غير المعتادة Mohamed Adel Hosny ; Supervised L. F. Abdelelal , N. H. Sweilam , M. M. Khader - Cairo : Mohamed Adel Hosny , 2014 - 136 P. ; 25cm
Thesis (Ph.D.) - Cairo University - Faculty of Science - Department of Mathematics
This thesis is a contribution on numerical studies for anomalous subdiffusion equations. A class of numerical methods for solving two of the most important anomalous subdiffusion equations which are the fractional cable equation (FCE) of spiny neuronal dendrites and the fractional reaction - subdiffusion equation (FRSE) is presented. This class of methods is very close to the weighted average finite difference method (WAFDM). Theorems with their proofs are presented to study the stability analysis and the truncation error of the proposed method. Also, a numerical method depends on the finite difference method based on Hermite formula is presented to solve two of the anomalous subdiffusion equations which are the fractional reaction - subdiffusion equation and the fractional diffusion - wave equation
Anomalous subdiffusion equations Fractional diffusion Mathematics