On efficient numerical solution of one-dimensional convection diffusion equations in modelling atmospheric processes

2008 ◽  
Vol 32 (2) ◽  
pp. 231 ◽  
Author(s):  
Vitaliy A. Prusov ◽  
Anatoliy Yu. Doroshenko
Keyword(s):  
Numerical Solution ◽  
Diffusion Equations ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Atmospheric Processes

A Finite-Element Singular-Perturbation Technique for Convection-Diffusion Problems—Part 1: The One-Dimensional Case

1981 ◽  
Vol 48 (2) ◽  
pp. 265-271 ◽  
Author(s):  
Rafael F. Diaz-Munio ◽  
L. Carter Wellford
Keyword(s):  
Finite Element ◽  
Singular Perturbation ◽  
Perturbation Technique ◽  
Diffusion Equations ◽  
Shape Functions ◽  
Singular Perturbation Technique ◽  
One Dimensional ◽  
Convection Diffusion ◽  
The One ◽  
Standard Galerkin Method

Approximation procedures for the solution of convection-diffusion equations, occurring in various physical problems, are considered. Several finite-element algorithms based on singular-perturbation methods are proposed for the solution of these equations. A method of variational matched asymptotic expansions is employed to develop shape functions which are particularly useful when convection effects dominate diffusion effects in these problems. When these shape functions are used, in conjunction with the standard Galerkin method, to solve convection-diffusion equations, increased solution accuracy is obtained. Numerical results for various one-dimensional problems are presented to establish the workability of the developed methods.

Numerical solution for a class of fractional convection–diffusion equations using the flatlet oblique multiwavelets

2013 ◽  
Vol 20 (6) ◽  
pp. 913-924 ◽  
Author(s):  
Safar Irandoust-pakchin ◽  
Mehdi Dehghan ◽  
Somayeh Abdi-mazraeh ◽  
Mehrdad Lakestani
Keyword(s):  
Numerical Solution ◽  
Diffusion Equations ◽  
Convection Diffusion

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.

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