Numerical solution for the time-fractional Fokker–Planck equation via shifted Chebyshev polynomials of the fourth kind
Haile Habenom, D. L. Suthar
Abstract
Abstract This paper provides a numerical approach for solving the time-fractional Fokker–Planck equation (FFPE). The authors use the shifted Chebyshev collocation method and the finite difference method (FDM) to present the fractional Fokker–Planck equation into systems of nonlinear equations; the Newton–Raphson method is used to produce approximate results for the nonlinear systems. The results obtained from the FFPE demonstrate the simplicity and efficiency of the proposed method.
Topics & Concepts
Chebyshev polynomialsCollocation (remote sensing)MathematicsFokker–Planck equationChebyshev filterNonlinear systemApplied mathematicsFractional calculusCollocation methodChebyshev equationMathematical analysisChebyshev iterationChebyshev pseudospectral methodOrthogonal polynomialsClassical orthogonal polynomialsPhysicsPartial differential equationDifferential equationComputer scienceQuantum mechanicsMachine learningOrdinary differential equationFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsMathematical functions and polynomials