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Original Articles

Family of quadratic spline difference schemes for a convection–diffusion problem

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Pages 33-50 | Received 11 Oct 2005, Accepted 13 Nov 2006, Published online: 29 Mar 2007
 

Abstract

We consider the finite difference approximation of a singularly perturbed one-dimensional convection–diffusion two-point boundary value problem. It is discretized using quadratic splines as approximation functions, equations with various piecewise constant coefficients as collocation equations and a piecewise uniform mesh of Shishkin type. The family of schemes is derived using the collocation method. The numerical methods developed here are non-monotone and therefore apart from the consistency error we use Green's grid function analysis to prove uniform convergence. We prove the almost first order of convergence and furthermore show that some of the schemes have almost second-order convergence. Numerical experiments presented in the paper confirm our theoretical results.

Acknowledgements

This paper was supported by the Ministry of Science, Republic of Serbia, under grant No. 144006.

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