The applications of non-polynomial spline to the numerical solution for fractional differential equations
Faraidun K. Hamasalh, Mizhda Abbas Headayat
Abstract
This paper presents a computation and discuss on non-polynomial spline of fractional order to solve the differential equations with Caputo fractional derivative. Taylor series is applied to discretize the time derivative of the function. Several examples are considered to confirm the accuracy of the spline method and to show the completion of non-polynomial spline. In addition, we discuss the numerical computations provident and can be used to solve complex problems, also the results are obtained to be in a nice error estimation with known exact solutions.
Topics & Concepts
Spline (mechanical)DiscretizationComputationApplied mathematicsTaylor seriesM-splinePolynomialThin plate splineHermite splineDifferential equationFractional calculusMathematicsPerfect splineComputer scienceMathematical analysisSpline interpolationAlgorithmStructural engineeringEngineeringBilinear interpolationStatisticsFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsDifferential Equations and Numerical Methods