Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (2)

Search Parameters:
Keywords = enhanced unconditionally positive finite difference method

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
23 pages, 1420 KB  
Article
Solving the Advection Diffusion Reaction Equations by Using the Enhanced Higher-Order Unconditionally Positive Finite Difference Method
by Ndivhuwo Ndou, Phumlani Dlamini and Byron Alexander Jacobs
Mathematics 2024, 12(7), 1009; https://doi.org/10.3390/math12071009 - 28 Mar 2024
Cited by 1 | Viewed by 3027
Abstract
In this paper, the enhanced higher-order unconditionally positive finite difference method is developed to solve the linear, non-linear and system advection diffusion reaction equations. Investigation into the effectiveness and efficiency of the proposed method is carried out by calculating the convergence rate, error [...] Read more.
In this paper, the enhanced higher-order unconditionally positive finite difference method is developed to solve the linear, non-linear and system advection diffusion reaction equations. Investigation into the effectiveness and efficiency of the proposed method is carried out by calculating the convergence rate, error and computational time. A comparison of the solutions obtained by the enhanced higher-order unconditionally positive finite difference and exact solution is conducted for validation purposes. The numerical results show that the developed method reduced the time taken to solve the linear and non-linear advection diffusion reaction equations as compared to the results obtained by the higher-order unconditionally positive finite difference method. Full article
(This article belongs to the Section E: Applied Mathematics)
Show Figures

Figure 1

18 pages, 1064 KB  
Article
Enhanced Unconditionally Positive Finite Difference Method for Advection–Diffusion–Reaction Equations
by Ndivhuwo Ndou, Phumlani Dlamini and Byron Alexander Jacobs
Mathematics 2022, 10(15), 2639; https://doi.org/10.3390/math10152639 - 27 Jul 2022
Cited by 15 | Viewed by 2387
Abstract
In this study, we develop the enhanced unconditionally positive finite difference method (EUPFD), and use it to solve linear and nonlinear advection–diffusion–reaction (ADR) equations. This method incorporates the proper orthogonal decomposition technique to the unconditionally positive finite difference method (UPFD) to reduce the [...] Read more.
In this study, we develop the enhanced unconditionally positive finite difference method (EUPFD), and use it to solve linear and nonlinear advection–diffusion–reaction (ADR) equations. This method incorporates the proper orthogonal decomposition technique to the unconditionally positive finite difference method (UPFD) to reduce the degree of freedom of the ADR equations. We investigate the efficiency and effectiveness of the proposed method by checking the error, convergence rate, and computational time that the method takes to converge to the exact solution. Solutions obtained by the EUPFD were compared with the exact solutions for validation purposes. The agreement between the solutions means the proposed method effectively solved the ADR equations. The numerical results show that the proposed method greatly improves computational efficiency without a significant loss in accuracy for solving linear and nonlinear ADR equations. Full article
(This article belongs to the Special Issue Numerical Methods for Computational Fluid Dynamics)
Show Figures

Figure 1

Back to TopTop