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An Efficient Collocation Technique for Solving Generalized Fokker-Planck Type Equations With Variable Coefficients

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2014

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Editura Academiei Romane

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Abstract

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.

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Generalized Fokker-Plank Equation, Collocation Method, Real Newell-Whitehead Equation, Implicit Runge-Kutta Method, Time-Dependent Fokker-Plank Equation

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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).

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Proceedings of the Romanian Academy Series A - Mathematics Physics Technical Sciences Information Science

Volume

14

Issue

4

Start Page

322

End Page

330