# Retraction: [Numerical Solution to Unsteady One-Dimensional Convection-Diffusion Problems Using Compact Difference Schemes Combined with Runge-Kutta Methods]

## Authors

• Zhenwei Zhu Department of Energy and Power Engineering, School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo, Henan, China https://orcid.org/0000-0001-7719-2475
• Junjie Chen Department of Energy and Power Engineering, School of Mechanical and Power Engineering, Henan Polytechnic University, Jiaozuo, Henan, China https://orcid.org/0000-0002-4222-1798

## Keywords:

Runge-Kutta methods, compact finite difference schemes, convection-diffusion equations, stability analysis, high-order accuracy, Crank-Nicolson methods

## Abstract

Retraction Note: Volume 3, Issue 3, CM-1691

DOI: https://doi.org/10.37256/cm.3320221691

The convection-diffusion equation is of primary importance in understanding transport phenomena within a physical system. However, the currently available methods for solving unsteady convection-diffusion problems are generally not able to offer excellent accuracy in both time and space variables. A procedure was given in detail to solve the unsteady one-dimensional convection-diffusion equation through a combination of Runge-Kutta methods and compact difference schemes. The combination method has fourth-order accuracy in both time and space variables. Numerical experiments were conducted and the results were compared with those obtained by the Crank-Nicolson method in order to check the accuracy of the combination method. The analysis results indicated that the combination method is numerically stable at low wave numbers and small CFL numbers. The combination method has higher accuracy than the Crank-Nicolson method.

2021-11-18

## How to Cite

1.
Zhu Z, Chen J. Retraction: [Numerical Solution to Unsteady One-Dimensional Convection-Diffusion Problems Using Compact Difference Schemes Combined with Runge-Kutta Methods]. Contemp. Math. [Internet]. 2021 Nov. 18 [cited 2024 Jul. 18];2(4):399-408. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/1167

Research Article