Analysis and Petrov–Galerkin numerical approximation for variable coefficient two-sided fractional diffusion, advection, reaction equations

Numerical Solution of Advection-Diffusion-Reaction Equations

Numerical solutions for fractional reaction-diffusion equations

Fractional diffusion equations are useful for applications where a cloud of particles spreads faster than the classical equation predicts. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative of order less than two. The resulting solutions spread faster than the classical solutions and may exhibit asymmetry, depending on the fr...

Approximation of stochastic advection diffusion equations with finite difference scheme

In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...

Numerical Solving Two-dimensional Variable-order Fractional Advection-dispersion Equation

Abstract: In this paper, a two-dimensional variable-order fractional advection-dispersion equation with variable coefficient is considered. The numerical method with first order temporal accuracy and first order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by using energy method. Finally, the results of a numerical example supports the theoret...

Presentation of two models for the numerical analysis of fractional integro-differential equations and their comparison

In this paper, we exhibit two methods to numerically solve the fractional integro differential equations and then proceed to compare the results of their applications on different problems. For this purpose, at first shifted Jacobi polynomials are introduced and then operational matrices of the shifted Jacobi polynomials are stated. Then these equations are solved by two methods: Caputo fractio...