Modified Three-Point Fractional Formulas with Richardson Extrapolation
Iqbal M. Batiha, Shameseddin Alshorm, Adel Ouannas, Shaher Momani, Osama Y. Ababneh, Meaad Albdareen
Abstract
In this paper, we introduce new three-point fractional formulas which represent three generalizations for the well-known classical three-point formulas; central, forward and backward formulas. This has enabled us to study the function’s behavior according to different fractional-order values of α numerically. Accordingly, we then introduce a new methodology for Richardson extrapolation depending on the fractional central formula in order to obtain a high accuracy for the gained approximations. We compare the efficiency of the proposed methods by using tables and figures to show their reliability.
Topics & Concepts
ExtrapolationRichardson extrapolationMathematicsApplied mathematicsPoint (geometry)Reliability (semiconductor)Fractional calculusOrder (exchange)Function (biology)Calculus (dental)Mathematical analysisGeometryPhysicsEconomicsEvolutionary biologyBiologyFinanceMedicineQuantum mechanicsDentistryPower (physics)Fractional Differential Equations SolutionsAdvanced Control Systems DesignIterative Methods for Nonlinear Equations