The use of He's variational iteration method for solving a Fokker–Planck equation
- 3 August 2006
- journal article
- Published by IOP Publishing in Physica Scripta
- Vol. 74 (3), 310-316
- https://doi.org/10.1088/0031-8949/74/3/003
Abstract
This paper applies the variational iteration method to an initial value problem of parabolic type. This method is based on the use of Lagrange multipliers for identification of optimal values of parameters in a functional. This method is a powerful tool for solving various kinds of problems. Employing this technique, it is possible to find the exact solution or an approximate solution of the problem. Using the variational iteration method of He, a rapid convergent sequence is produced which tends to the exact solution of the problem. The results of this method are the same as with the results obtained by the Adomian decomposition method. The fact that this technique solves nonlinear equations without using Adomian polynomials can be considered as an advantage of this method over the Adomian decomposition procedure. The linear and nonlinear cases of the Fokker–Planck equation are considered and solved using the variational iteration method. To show the efficiency of the variational iteration method, several examples are presented.Keywords
This publication has 27 references indexed in Scilit:
- Analytical approach to linear fractional partial differential equations arising in fluid mechanicsPhysics Letters A, 2006
- The application of He's homotopy perturbation method to nonlinear equations arising in heat transferPhysics Letters A, 2006
- Application of He’s variational iteration method to Helmholtz equationChaos, Solitons, and Fractals, 2006
- Variational iteration method for solving Burger's and coupled Burger's equationsJournal of Computational and Applied Mathematics, 2005
- An iteration formulation for normalized diode characteristicsInternational Journal of Circuit Theory and Applications, 2004
- Variational iteration method for autonomous ordinary differential systemsApplied Mathematics and Computation, 2000
- Variational iteration method – a kind of non-linear analytical technique: some examplesInternational Journal of Non-Linear Mechanics, 1999
- Approximate analytical solution for seepage flow with fractional derivatives in porous mediaComputer Methods in Applied Mechanics and Engineering, 1998
- Approximate solution of nonlinear differential equations with convolution product nonlinearitiesComputer Methods in Applied Mechanics and Engineering, 1998
- Variational iteration method for delay differential equationsCommunications in Nonlinear Science and Numerical Simulation, 1997