A Spectrally Accurate Step-by-Step Method for the Numerical Solution of Fractional Differential Equations
Luigi Brugnano, Kevin Burrage, Pamela Burrage, Felice Iavernaro
Abstract
Abstract In this paper we consider the numerical solution of fractional differential equations. In particular, we study a step-by-step procedure, defined over a graded mesh, which is based on a truncated expansion of the vector field along the orthonormal Jacobi polynomial basis. Under mild hypotheses, the proposed procedure is capable of getting spectral accuracy. A few numerical examples are reported to confirm the theoretical findings.
Topics & Concepts
MathematicsMathematical analysisNumerical analysisFractional calculusDifferential equationApplied mathematicsCalculus (dental)MedicineDentistryFractional Differential Equations SolutionsNumerical methods for differential equationsDifferential Equations and Numerical Methods