A third-order semi-implicit finite difference method for solving the one-dimensional convection-diffusion equation

1988 ◽  
Vol 26 (7) ◽  
pp. 1615-1629 ◽  
Author(s):  
B. J. Noye ◽  
H. H. Tan
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Difference Method ◽  
Third Order ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Implicit Finite Difference ◽  
The One

scholarly journals On the numerical solution of the one-dimensional convection-diffusion equation

2005 ◽  
Vol 2005 (1) ◽  
pp. 61-74 ◽  
Author(s):  
Mehdi Dehghan
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Difference ◽  
Diffusion Equation ◽  
Numerical Solution ◽  
Partial Differential ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
The One

The numerical solution of convection-diffusion transport problems arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flow, in the modeling of semiconductors, and so forth. This paper describes several finite difference schemes for solving the one-dimensional convection-diffusion equation with constant coefficients. In this research the use of modified equivalent partial differential equation (MEPDE) as a means of estimating the order of accuracy of a given finite difference technique is emphasized. This approach can unify the deduction of arbitrary techniques for the numerical solution of convection-diffusion equation. It is also used to develop new methods of high accuracy. This approach allows simple comparison of the errors associated with the partial differential equation. Various difference approximations are derived for the one-dimensional constant coefficient convection-diffusion equation. The results of a numerical experiment are provided, to verify the efficiency of the designed new algorithms. The paper ends with a concluding remark.

scholarly journals A new formulation of finite difference and finite volume methods for solving a space fractional convection–diffusion model with fewer error estimates

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Reem Edwan ◽  
Shrideh Al-Omari ◽  
Mohammed Al-Smadi ◽  
Shaher Momani ◽  
Andreea Fulga
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Finite Volume ◽  
Difference Method ◽  
Order Accuracy ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
The Finite Difference Method ◽  
Volume Method

AbstractConvection and diffusion are two harmonious physical processes that transfer particles and physical quantities. This paper deals with a new aspect of solving the convection–diffusion equation in fractional order using the finite volume method and the finite difference method. In this context, we present an alternative way for estimating the space fractional derivative by utilizing the fractional Grünwald formula. The proposed methods are conditionally stable with second-order accuracy in space and first-order accuracy in time. Many comparisons are performed to display reliability and capability of the proposed methods. Furthermore, several results and conclusions are provided to indicate appropriateness of the finite volume method in solving the space fractional convection–diffusion equation compared with the finite difference method.

scholarly journals A Hybrid Differential Transforms and Finite Difference Method to Numerical Solution of Convection–Diffusion Equation

2021 ◽  
Vol 8 (6) ◽  
pp. 90-94
Author(s):  
Noorulhaq Ahmadi ◽  
Mohammadi Khan Mohammadi
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Difference Method ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Type Boundary

In this work, we discuss a hybrid-based method on differential transforms and a finite difference method to numerical solution of convection–diffusion equation with Dirichlet’s type boundary conditions. The developed method is tested on various problems and the numerical results are reported in tabular and figure form. This method can be easily extended to handle non-linear convection–diffusion partial differential equations.

scholarly journals A Weighted Average Finite Difference Method for the Fractional Convection-Diffusion Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Lijuan Su ◽  
Pei Cheng
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Difference Method ◽  
Average Method ◽  
Weighted Average ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Weighted Average Method ◽  
Weighted Factor

A weighted average finite difference method for solving the two-sided space-fractional convection-diffusion equation is given, which is an extension of the weighted average method for ordinary convection-diffusion equations. Stability, consistency, and convergence of the new method are analyzed. A simple and accurate stability criterion valid for this method, arbitrary weighted factor, and arbitrary fractional derivative is given. Some numerical examples with known exact solutions are provided.

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