Numerical Methods for the Time Fractional Convection-Diffusion-Reaction Equation
Changpin Li, Zhen Wang
Abstract
In this article, efficient methods are derived for seeking numerical solution to the time fractional convection-diffusion-reaction equation whose solution very likely exhibits a weak regularity at the starting time. Here, the time fractional derivative in the Caputo sense with order in (0, 1) is discretized by the finite difference methods with uniform and non-uniform meshes and the spatial derivative by the local discontinuous Galerkin finite element method. The derived numerical schemes are stable and convergent. Finally, some numerical experiments are presented to verify the theoretical analysis.
Topics & Concepts
MathematicsDiscretizationConvection–diffusion equationFractional calculusMathematical analysisFinite element methodDiscontinuous Galerkin methodTime derivativeNumerical solution of the convection–diffusion equationNumerical analysisReaction–diffusion systemPolygon meshDerivative (finance)Material derivativeGalerkin methodApplied mathematicsDiffusionFinite difference methodMixed finite element methodGeometryPhysicsEconomicsThermodynamicsFinancial economicsFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsIterative Methods for Nonlinear Equations