High-order numerical method for two-dimensional Riesz space fractional advection-dispersion equation
A. Borhanifar, Maria Alessandra Ragusa, Sohrab Valizadeh
Abstract
<p style='text-indent:20px;'>In this paper, by combining of fractional centered difference approach with alternating direction implicit method, we introduce a mixed difference method for solving two-dimensional Riesz space fractional advection-dispersion equation. The proposed method is a fourth order centered difference operator in spatial directions and second order Crank-Nicolson method in temporal direction. By reviewing the consistency and stability of the method, the convergence of the proposed method is achieved. Several numerical examples are considered aiming to demonstrate the validity and applicability of the proposed technique.
Topics & Concepts
MathematicsConvergence (economics)AdvectionOperator (biology)Stability (learning theory)Space (punctuation)Consistency (knowledge bases)Dispersion (optics)Mathematical analysisApplied mathematicsOrder (exchange)Computer sciencePhysicsGeometryOpticsRepressorChemistryOperating systemFinanceThermodynamicsMachine learningEconomic growthTranscription factorBiochemistryGeneEconomicsFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsDifferential Equations and Numerical Methods