190
Views
11
CrossRef citations to date
0
Altmetric
Original Articles

A novel three-level time-split MacCormack scheme for two-dimensional evolutionary linear convection-diffusion-reaction equation with source term

Pages 47-74 | Received 26 Jul 2019, Accepted 01 Feb 2020, Published online: 16 Feb 2020
 

ABSTRACT

This study presents a three-level explicit time-split MacCormack method to compute approximate solutions of two-dimensional time-dependent linear convection-diffusion-reaction equations with source term. The difference operators split the two-dimensional problem into two pieces so that each subproblem is easily solvable using the original MacCormack approach. Second order accuracy in time and fourth-order convergence in space are achieved by the application of the Taylor series expansion. The proposed algorithm minimizes the computational time, computer memory requirement and is easy to implement. Under a suitable time-step restriction, both stability and error estimates of the numerical scheme are deeply analysed in L(0,T;L2)-norm. Numerical evidences which confirm the theoretical analysis are considered and discussed.

AMS Subject Classification (MSC):

Acknowledgements

The author appreciates the comments of the anonymous referees which helped to improve the numerical evidences presented in this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.