Lin, J., Xu, Y. and Zhang, Y. (2020) Simulation of Linear and Nonlinear Advection-Diffusion-Reaction Problems by a Novel Localized Scheme. Applied Mathematics Letters, 99, 106005.
https://doi.org/10.1016/j.aml.2019.106005

has been cited by the following article:

• TITLE: Higher Order Implicit Scheme for Nonlinear Time-Dependent Convection-Diffusion- Reaction Equation

  AUTHORS: Uzair Ahmed, Daoud Suleiman Mashat, Dalal Adnan Maturi

  KEYWORDS: Finite Difference Method (FDM), Crank-Nicholson (CN), Fourth Order Implicit (FOI), Convection-Diffusion-Reaction (CDR)

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.12 No.2, June 10, 2022

  ABSTRACT: A mathematical model comprising of nonlinear reaction, diffusion, and convection mechanisms seen in natural and anthropogenic processes is numerically investigated here. It is proposed that a higher order numerical scheme of finite difference method be used in conjunction with an iterative approach in order to solve the nonlinear one dimensional convection-diffusion-reaction equation. To account for the wide variety of physical characteristics and boundary conditions, an iterative approach is presented that yields a reliable and precise solution every time. We examined the accuracy and operational efficiency of two distinct finite difference approaches. The efficiency of the system is determined by comparing the estimated results to the appropriate analytical solution by adhering to established norms. Coherence and convergence were analyzed for each approach. The simulation results demonstrate the efficacy and accuracy of these methods in solving nonlinear convection- diffusion-reaction equations. Convection-diffusion-reaction equation modeling is critical for employing the offered results in heat and mass transport processes.