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Homotopy perturbation method Fokker-Planck equation. (English) Zbl 1165.82020
The paper considers the application of the homotopy perturbation method introduced by [J. H. He, Comput. Math. Appl. Mech. Eng. 178, 257–262 (1999; Zbl 0956.70017)] to obtain the exact solution of examples of linear and nonlinear Fokker-Planck equations considered in [M. Tatari, M. Dehghan and M. Razzaghi, Math. Comput. Model. 45, 639–650 (2007; Zbl 1165.65397)] by means of the Adomian decomposition method. This technique does not require a small parameter in the equation. According to the homotopy technique, a homotopy with an imbedding parameter \(p\in [0,1]\) is constructed, and the imbedding parameter is considered as a “small parameter”, so that the method is called the homotopy perturbation method.

MSC:
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
35A35 Theoretical approximation in context of PDEs
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