AN EFFICIENT COLLOCATION TECHNIQUE FOR SOLVING GENERALIZED FOKKER-PLANCK TYPE EQUATIONS WITH VARIABLE COEFFICIENTS

作者：Bhrawy A H^*; Ahmed Engy A; Baleanu D

来源：Proceedings of the Romanian Academy - Series A: Mathematics, Physics, Technical Sciences, Information Science , 2014, 15(4): 322-330.

• time-dependent Fokker-Plank equation
• generalized Fokker-Plank equation
• real Newell-Whitehead equation
• collocation method
• implicit Runge-Kutta method

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 alpha and beta. Using the above technique, the problem is reduced to the solution of a system of ordinary differential equations in tithe. 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.

• 出版日期2014-12