Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
Numerical solutions of a Michaelis--Menten-type ratio-dependent predator--prey system with diffusion
Applied Numerical Mathematics
Higher-order compact finite difference method for systems of reaction-diffusion equations
Journal of Computational and Applied Mathematics
Error and extrapolation of a compact LOD method for parabolic differential equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
A numerical scheme for particle-laden thin film flow in two dimensions
Journal of Computational Physics
Computers & Mathematics with Applications
Existence and Asymptotic Behavior of Solutions for Quasilinear Parabolic Systems
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Hi-index | 0.01 |
This paper is concerned with numerical solutions of a general class of coupled nonlinear parabolic equations by the finite difference method. Three monotone iteration processes for the finite difference system are presented, and the sequences of iterations are shown to converge monotonically to a unique solution of the system, including an existence-uniqueness-comparison theorem. A theoretical comparison result for the various monotone sequences and an error analysis of the three monotone iterative schemes are given. Also given is the convergence of the finite difference solution to the continuous solution of the parabolic boundary-value problem. An application to a reaction-diffusion model in chemical engineering and combustion theory is given.