Optimal Hermite collocation applied to a one‐dimensional convection‐diffusion equation using an adaptive hybrid optimization algorithm

2009 ◽  
Vol 19 (7) ◽  
pp. 874-893 ◽  
Author(s):  
Karen L. Ricciardi ◽  
Stephen H. Brill
Keyword(s):  
Diffusion Equation ◽  
Optimization Algorithm ◽  
Hybrid Optimization ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Hybrid Optimization Algorithm

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 Entropy Schemes for One-Dimensional Convection-Diffusion Equations

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Rongsan Chen
Keyword(s):  
Diffusion Equation ◽  
Hyperbolic Conservation Laws ◽  
Operator Splitting ◽  
Splitting Method ◽  
Order Accuracy ◽  
Central Difference ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Operator Splitting Method

In this paper, we extend the entropy scheme for hyperbolic conservation laws to one-dimensional convection-diffusion equation. The operator splitting method is used to solve the convection-diffusion equation that is divided into conservation and diffusion parts, in which the first-order accurate entropy scheme is applied to solve the conservation part and the second accurate central difference scheme is applied to solve the diffusion part. Numerical tests show that the L∞ error achieves about second-order accuracy, but the L1 error reaches about forth-order accuracy.

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