Abstract
In this paper, a numerical method for the solution of a strongly coupled reaction-diffusion system, with suitable initial and Neumann boundary conditions, by using cubic B-spline collocation scheme on a uniform grid is presented. The scheme is based on the usual finite difference scheme to discretize the time derivative while cubic B-spline is used as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann method. The accuracy of the proposed scheme is demonstrated by applying it on a test problem. The performance of this scheme is shown by computing and error norms for different time levels. The numerical results are found to be in good agreement with known exact solutions.
Highlights
This study is concerned with the numerical solution of strongly coupled reaction-diffusion system using cubic B-spline
It can be used to describe a mathematical model of a class of chemical exchange reaction that arises in the transport of ground water in an aquifer [1]
A2(0)~v’0(0), b2(0)~v’0(1): The global solutions of such a system of equations have attracted the attention of several researchers [2,3,4,5,6]
Summary
This study is concerned with the numerical solution of strongly coupled reaction-diffusion system using cubic B-spline. Cao and Sun [1] derived a finite difference scheme by the method of reduction of order for the numerical solution of strongly coupled reaction-diffusion system with Neumann boundary values conditions. They proved the solvability and convergence by using the energy method. The solution of the system was calculated in the form of an infinite series with computed components This method cannot always guarantee the convergence of approximate series [8,9] and the method depends on choosing the proper linear operator and initial guesses
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