New Algorithms for Dealing with Fractional Initial Value Problems
Iqbal M. Batiha, Ahmad A. Abubaker, Iqbal H. Jebril, Suha B. Al-Shaikh, Khaled Matarneh
Abstract
This work purposes to establish two small numerical modifications for the Fractional Euler method (FEM) and the Modified Fractional Euler Method (MFEM) to deal with fractional initial value problems. Two such modifications, which are named Improved Modified Fractional Euler Method 1 (IMFEM 1) and Improved Modified Fractional Euler Method 2 (IMFEM 2), endeavor to further enhance FEM and MFEM in terms of attaining more accuracy. By utilizing certain theoretical results, the resultant error bounds of the proposed methods are analyzed and estimated. Several numerical comparisons are carried out to validate the efficiency of our proposed methods.
Topics & Concepts
Euler's formulaFinite element methodMathematicsApplied mathematicsFractional calculusValue (mathematics)AlgorithmEuler methodNumerical analysisWork (physics)Mathematical optimizationComputer scienceMathematical analysisStatisticsStructural engineeringEngineeringMechanical engineeringFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsNumerical methods for differential equations