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.