High-order numerical method for two-dimensional Riesz space fractional advection-dispersion equation
نویسندگان
چکیده
In this paper, by combining of fractional centered difference approach with alternating direction implicit method, we introduce a mixed method for solving two-dimensional Riesz space advection-dispersion equation. The proposed is fourth order operator in spatial directions and second Crank-Nicolson temporal direction. By reviewing the consistency stability convergence achieved. Several numerical examples are considered aiming to demonstrate validity applicability technique.
منابع مشابه
A numerical scheme for space-time fractional advection-dispersion equation
In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. We utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. By using Bernstein polynomial basis, the problem is transformed in...
متن کاملNumerical 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...
متن کاملa numerical scheme for space-time fractional advection-dispersion equation
in this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. we utilize spectral-collocation method combining with a product integration technique in order to discretize the terms involving spatial fractional order derivatives that leads to a simple evaluation of the related terms. by using bernstein polynomial basis, the problem is transformed in...
متن کاملA numerical scheme for space-time fractional advection-dispersion equation
In this paper, we develop a numerical resolution of the space-time fractional advection-dispersion equation. After time discretization, we utilize collocation technique and implement a product integration method in order to simplify the evaluation of the terms involving spatial fractional order derivatives. Then utilizing Bernstein polynomials as basis, the problem is transformed into a linear ...
متن کاملNumerical approximation of a one-dimensional space fractional advection-dispersion equation with boundary layer
Finite element computations for singularly perturbed convection-diffusion equations have long been an attractive theme for numerical analysis. In this article, we consider the singularly perturbed fractional advection-dispersion equation (FADE) with boundary layer behavior. We derive a theoretical estimate which shows that the under-resolved case corresponds to ǫ < hα−1, where α is the order of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems-series B
سال: 2021
ISSN: ['1531-3492', '1553-524X']
DOI: https://doi.org/10.3934/dcdsb.2020355