Jacobi collocation method for the fractional advection‐dispersion equation arising in porous media
Harendra Singh
Abstract
In present paper, we solve fractional advection-dispersion equation (ADE) using Jacobi collocation method. This equation appears in the transport of solutes in ground water and soils. Using Jacobi spectral collocation method the fractional ADE is converted into systems of nonlinear algebraic equations whose solution leads the approximate solution for this equation. We provide the convergence analysis of the proposed approximate method. The applicability of proposed method is shown by testing it on some illustrative examples. Numerical results are shown using figures. Absolute error figures show the accuracy of the proposed method. CPU time is also listed in tabular form to show efficiency of the proposed method.
Topics & Concepts
MathematicsCollocation methodCollocation (remote sensing)Convergence (economics)Orthogonal collocationDispersion (optics)Algebraic equationJacobi methodAdvectionPorous mediumApplied mathematicsSpectral methodMathematical analysisNonlinear systemPorosityComputer scienceDifferential equationPhysicsChemistryOrganic chemistryMachine learningOpticsEconomic growthOrdinary differential equationThermodynamicsEconomicsQuantum mechanicsFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsNumerical methods in engineering