Fourth-Order Difference Approximation for Time-Fractional Modified Sub-Diffusion Equation
Umair Ali, Muhammad Sohail, Muhammad Usman, Farah Aini Abdullah, Ilyas Khan, Kottakkaran Sooppy Nisar
Abstract
Fractional differential equations describe nature adequately because of the symmetry properties which describe physical and biological processes. In this article, a fourth-order new implicit difference scheme is formulated and applied to solve the two-dimensional time-fractional modified sub-diffusion equation involving two times Riemann–Liouville fractional derivatives. The stability of the fourth-order implicit difference scheme is investigated using the von Neumann technique. The proposed scheme is shown to be unconditionally stable. Numerical examples are given to illustrate the feasibility of the proposed scheme.
Topics & Concepts
MathematicsScheme (mathematics)Stability (learning theory)Fractional calculusOrder (exchange)Applied mathematicsDifferential equationSymmetry (geometry)Von Neumann stability analysisMathematical analysisDiffusionNumerical analysisNumerical stabilityPhysicsComputer scienceQuantum mechanicsGeometryEconomicsFinanceMachine learningFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsNonlinear Differential Equations Analysis