Browsing by Author "Ahmed, Engy A."

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Citation Count: Hafez, R.M...et al. (2015). A Jacobi Gauss-Lobatto and Gauss-Radau collocation algorithm for solving fractional Fokker-Planck equations. Nonlinear Dynamics, 82(3), 1431-1440. http://dx.doi.org/10.1007/s11071-015-2250-7
A Jacobi Gauss-Lobatto and Gauss-Radau collocation algorithm for solving fractional Fokker-Planck equations
(Springer, 2015) Hafez, R. M.; Ezz-Eldien, Samer S.; Bhrawy, Ali H.; Ahmed, Engy A.; Baleanu, Dumitru
In this article, we construct a new numerical approach for solving the time-fractional Fokker-Planck equation. The shifted Jacobi polynomials are used as basis functions, and the fractional derivative is described in the sense of Caputo. The proposed approach is a combination of shifted Jacobi Gauss-Lobatto scheme for the spatial discretization and the shifted Jacobi Gauss-Radau scheme for temporal approximation. The problem is then reduced to a problem consisting of a system of algebraic equations that greatly simplifies the problem. In addition, our numerical algorithm is also applied for solving the space-fractional Fokker-Planck equation and the time-space-fractional Fokker-Planck equation. Numerical results are consistent with the theoretical analysis, indicating the high accuracy and effectiveness of the proposed algorithm
Citation Count: Bhrawy, A.H.; Ahmed, E.A.; Baleanu, D.,"An Efficient Collocation Technique for Solving Generalized Fokker-Planck Type Equations With Variable Coefficients", Proceedings of the Romanian Academy Series A - Mathematics Physics Technical Sciences Information Science, Vol. 14, No. 4, pp. 322-330, (2014).
An Efficient Collocation Technique for Solving Generalized Fokker-Planck Type Equations With Variable Coefficients
(Editura Academiei Romane, 2014) Bhrawy, A. H.; Ahmed, Engy A.; Baleanu, Dumitru; 56389
This paper proposes an efficient numerical integration process for the generalized Fokker-Planck equation with variable coefficients. For spatial discretization the Jacobi-Gauss-Lobatto collocation (J-GL-C) method is implemented in which the Jacobi-Gauss-Lobatto points are used as collocation nodes for spatial derivatives. This approach has the advantage of obtaining the solution in terms of the Jacobi parameters α and β . Using the above technique, the problem is reduced to the solution of a system of ordinary differential equations in time. This system can be also solved by standard numerical techniques. Our results demonstrate that the proposed method is a powerful algorithm for solving nonlinear partial differential equations.