Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences
Alessandra Jannelli
Abstract
This paper deals with the numerical solutions of a class of fractional mathematical models arising in engineering sciences governed by time-fractional advection-diffusion-reaction (TF–ADR) equations, involving the Caputo derivative. In particular, we are interested in the models that link chemical and hydrodynamic processes. The aim of this paper is to propose a simple and robust implicit unconditionally stable finite difference method for solving the TF–ADR equations. The numerical results show that the proposed method is efficient, reliable and easy to implement from a computational viewpoint and can be employed for engineering sciences problems.
Topics & Concepts
Fractional calculusApplied mathematicsScience and engineeringSimple (philosophy)Numerical analysisMathematical sciencesComputer scienceMathematicsFinite difference methodClass (philosophy)AdvectionMathematical analysisEngineeringPhysicsEpistemologyMathematics educationEngineering ethicsPhilosophyThermodynamicsArtificial intelligenceFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsDifferential Equations and Numerical Methods