Numerical Solution of Fractional Integro-Differential Equations Via Fourth-Degree Hat Functions
Jehad K. Mohammed, Ayad R. Khudair
Abstract
The goal of this paper is to construct new fourth-degree hat functions (FDHFs) and study their properties in order to develop a new numerical method for solving fractional integro-differential equations. The equation under consideration is transformed into a set of algebraic equations by using FDHFs, which makes it simple to solve the system using one of the iterative methods. In fact, this method’s advantage was that it was easy to use and had fifth-order convergence, as we showed in the section on error analysis. The numerical results demonstrate that the new technique works well through the presented examples.
Topics & Concepts
MathematicsAlgebraic equationDegree (music)Convergence (economics)Numerical analysisSet (abstract data type)Differential equationApplied mathematicsSimple (philosophy)Iterative methodIntegral equationMathematical analysisComputer scienceMathematical optimizationNonlinear systemEconomic growthEpistemologyPhilosophyProgramming languagePhysicsQuantum mechanicsAcousticsEconomicsFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsDifferential Equations and Numerical Methods