A Fast Galerkin Approach for Solving the Fractional Rayleigh–Stokes Problem via Sixth-Kind Chebyshev Polynomials
Ahmed Gamal Atta, W. M. Abd‐Elhameed, Galal M. Moatimid, Y. H. Youssri
Abstract
Herein, a spectral Galerkin method for solving the fractional Rayleigh–Stokes problem involving a nonlinear source term is analyzed. Two kinds of basis functions that are related to the shifted sixth-kind Chebyshev polynomials are selected and utilized in the numerical treatment of the problem. Some specific integer and fractional derivative formulas are used to introduce our proposed numerical algorithm. Moreover, the stability and convergence accuracy are derived in detail. As a final validation of our theoretical results, we present a few numerical examples.
Topics & Concepts
MathematicsChebyshev polynomialsGalerkin methodConvergence (economics)Chebyshev filterFractional calculusChebyshev iterationSpectral methodApplied mathematicsStability (learning theory)Mathematical analysisNonlinear systemComputer sciencePhysicsEconomicsQuantum mechanicsMachine learningEconomic growthFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsNumerical methods in engineering