Numerical solution of Fokker‐Planck equation using the cubic B‐spline scaling functions

Abstract

In this article a numerical technique is presented for the solution of Fokker--Planck equation. This method uses the cubic B-spline scaling functions. The method consists of expanding the required approximate solution as the elements of cubic B-spline scaling function. Using the operational matrix of derivative, the problem will be reduced to a set of algebraic equations. Some numerical examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces very accurate results.

Meshless method for the numerical solution of the Fokker–Planck equation

“…Salehian et al [7] used the flatlet oblique multiwavelets for the solution of FokkerPlanck equation. Lakestani and Dehghan applied cubic Bspline scaling functions for solving Fokker-Planck equation [8]. Authors of [2] investigated the application of Adomian decomposition method for solving Fokker-Planck equation.…”

B spline-based method for 2-D large deformation analysis

“…In fact, a considerable body of literatures now exists on the application of uniform and non-uniform B spline techniques to the solution of partial differential equations (PDEs) and mechanics problems. The recent studies of B spline method can be found in some articles [17][18][19][20][21][22][23]. The B spline basis functions have compact support and lead to banded stiffness matrices.…”

A Novel Approach for Numerical Computation of Fokker-Planck Equation

“…Lakestani and Dehghan [5] has been applied cubic B-spline method to solve FPE and found that implementation of cubic B-spline method is easy and gives very accurate results. Palleschi et al [6] has been used a fast and accurate algorithm to obtain the numerical solution of FPE, and he also studied the stability and convergence of the algorithm analytically.…”