[HTML][HTML] Numerical approach of Fokker–Planck equation with Caputo–Fabrizio fractional derivative using Ritz approximation
Journal of Computational and Applied Mathematics, 2018•Elsevier
In this manuscript, a type of Fokker–Planck equation (FPE) with Caputo–Fabrizio fractional
derivative is considered. We present a numerical approach which is based on the Ritz
method with known basis functions to transform this equation into an optimization problem. It
leads to a nonlinear algebraic system. Then, we obtain the coefficients of basis functions by
solving the algebraic system. The convergence of this technique is discussed extensively.
Three examples are included to show the applicability and validity of this method.
derivative is considered. We present a numerical approach which is based on the Ritz
method with known basis functions to transform this equation into an optimization problem. It
leads to a nonlinear algebraic system. Then, we obtain the coefficients of basis functions by
solving the algebraic system. The convergence of this technique is discussed extensively.
Three examples are included to show the applicability and validity of this method.
Abstract
In this manuscript, a type of Fokker–Planck equation (FPE) with Caputo–Fabrizio fractional derivative is considered. We present a numerical approach which is based on the Ritz method with known basis functions to transform this equation into an optimization problem. It leads to a nonlinear algebraic system. Then, we obtain the coefficients of basis functions by solving the algebraic system. The convergence of this technique is discussed extensively. Three examples are included to show the applicability and validity of this method.
Elsevier