# Solving Fokker-Planck Equation By Two-Dimensional Differential Transform

2011-07-29
Cansu Kurt, Ümmügülsüm
Ozkan, Ozan
In this paper, we implement a reliable algorithm to obtain exact solutions for Fokker-Planck equation and some similar equations. The approach rests mainly on two dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions are obtained easily without linearizing the problem. Some illustrative examples are given to demonstrate the effectiveness of the presented method

# Suggestions

 Generalisation of the Lagrange multipliers for variational iterations applied to systems of differential equations ALTINTAN, DERYA; Uğur, Ömür (2011-11-01) In this paper, a new approach to the variational iteration method is introduced to solve systems of first-order differential equations. Since higher-order differential equations can almost always be converted into a first-order system of equations, the proposed method is still applicable to a wide range of differential equations. This generalised approach, unlike the classical method, uses restricted variations only for nonlinear terms by generalising the Lagrange multipliers. Consequently, this allows us t...
 Inverse problems for a semilinear heat equation with memory Kaya, Müjdat; Çelebi, Okay; Department of Mathematics (2005) In this thesis, we study the existence and uniqueness of the solutions of the inverse problems to identify the memory kernel k and the source term h, derived from First, we obtain the structural stability for k, when p=1 and the coefficient p, when g( )= . To identify the memory kernel, we find an operator equation after employing the half Fourier transformation. For the source term identification, we make use of the direct application of the final overdetermination conditions.
 The finite element method over a simple stabilizing grid applied to fluid flow problems Aydın, Selçuk Han; Tezer-Sezgin, Münevver; Department of Scientific Computing (2008) We consider the stabilized finite element method for solving the incompressible Navier-Stokes equations and the magnetohydrodynamic (MHD) equations in two dimensions. The well-known instabilities arising from the application of standard Galerkin finite element method are eliminated by using the stabilizing subgrid method (SSM), the streamline upwind Petrov-Galerkin (SUPG) method, and the two-level finite element method (TLFEM). The domain is discretized into a set of regular triangular elements. In SSM, the...
 Analysis of a projection-based variational multiscale method for a linearly extrapolated BDF2 time discretization of the Navier-Stokes equations Vargün, Duygu; Kaya Merdan, Songül; Department of Mathematics (2018) This thesis studies a projection-based variational multiscale (VMS) method based on a linearly extrapolated second order backward difference formula (BDF2) to simulate the incompressible time-dependent Navier-Stokes equations (NSE). The method concerns adding stabilization based on projection acting only on the small scales. To give a basic notion of the projection-based VMS method, a three-scale VMS method is explained. Also, the principles of the projection-based VMS stabilization are provided. By using t...
 Numerical Design of Testing Functions for the Magnetic-Field Integral Equation Karaosmanoglu, Bariscan; Ergül, Özgür Salih (2016-04-15) We present a novel numerical approach to design testing functions for the magnetic-field integral equation (MFIE). Enforcing the compatibility of matrix equations derived from MFIE and the electric-field integral equation (EFIE) for the same problem, testing weights for MFIE are determined on given templates of testing functions. The resulting MFIE systems produce more accurate results that the conventional MFIE implementations, without increasing the number of iterations and processing time. The design pro...
Citation Formats
Ü. Cansu Kurt and O. Ozkan, “Solving Fokker-Planck Equation By Two-Dimensional Differential Transform,” 2011, vol. 1368, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51508.