New Iterative Methods for Solving Fokker-Planck Equation

Abstract

In this article, we propose the new iterative method and introduce the integral iterative method to solve linear and nonlinear Fokker-Planck equations and some similar equations. The results obtained by the two methods are compared with those obtained by both Adomian decomposition and variational iteration methods. Comparison shows that the two methods are more effective and convenient to use and overcome the difficulties arising in calculating Adomian polynomials and Lagrange multipliers, which means that the considered methods can simply and successfully be applied to a large class of problems.

Numerical Treatment for the Three-Dimensional Eyring-Powell Fluid Flow over a Stretching Sheet with Velocity Slip and Activation Energy

“…Yao et al [35] developed a mathematical model for investigating the loss of root stone due water flow in dam structure. Hemeda et al [36] proposed an iterative technique along with integral iterative scheme for linear and nonlinear Fokker-Planck equations. Awad et al [37] used the time dependent rotating binary fluid flow over a suddenly stretched sheet using the enhanced Arrhenius function.…”

Analytical techniques for solving the equation governing the unsteady flow of a polytropic gas with time-fractional derivative

“…To illustrate the basic idea of this method, proposed first by Gejji and Jafari, consider the following general functional equation [18][19][20][21][22][23][24][25]:…”

“…Substituting (19) and the initial value u(0) = 0 into (40) and equating the terms of equal powers of p, we obtain the following set of fractional differential equations:…”

“…However, it is still very difficult to obtain closed-form solutions for most models of real-life problems. A broad class of analytical and numerical methods were used to handle such problems such as variational iteration method [1][2][3][4][5][6], Adomian decomposition method [7][8][9][10], homotopy perturbation method [11][12][13][14][15][16][17], new iterative method [18][19][20][21][22][23][24][25] and integral iterative method [26,27]. It is worth mentioning that the new iterative, homotopy perturbation and integral iterative methods are applied without any discretization, restrictive assumption or transformation and are free from round off errors.…”

A novel iterative method for solving chemical kinetics system

“…[22][23][24][25] Recently, a great attention has been given to the application of semi-analytical technique such as the iterative method (IM or DJM), which was introduced by Daftardar-Gejji and Jafari 26 and further modified by Bhalekar and Daftardar-Gejji. [27][28][29] Very recently, the IM was employed for solving various kinds of nonlinear mathematical problems that can be found in the following literatures. [30][31][32][33] In this research, we have applied the IM to unravel the nonlinear chemical kinetics equations.…”