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Home  >  Volume 38

9. Finite Difference Methods for the Numerical Approximations of One-dimensional Advection-diffusion-reaction Equation by Simple Implicit and Crank Nicolson Schemes by Ayodele Ojo, Ochoche A. Peter and Peter Bibian Volume 38, (November, 2016), pp 49 – 56
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Abstract

The One-dimensional Advection-diffusion-reaction equation considered in this paper was derived from the mass balance approach where the chemical being modeled was subjected to first-order decay reaction (dispersion). In this case, the parabolic partial differential equations with initial and boundary conditions can be approximated numerically. However, for the purpose of accuracy, two finite difference methods namely, the Simple Implicit and the Crank Nicolson schemes were employed. The former was found to be stable and convergent but it has the defect that, the time difference approximation is first-order accurate. Meanwhile, the later is unconditionally stable and second order accurate in both space and time. Also, the approximateresults obtainedshow an excellent agreement with the exact solution when computed for assumed values.Graphwas plotted to represents the comparison of the numerical results with the exact solution. This work is relevant to both scientific and engineering fields of study especially in finding the concentrations of a diffusive and advective substance in a given space per time.

Keywords: Advection, Diffusion, Accumulation, Dispersion,Crank Nicolson method, Implicit method, Stability

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