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Minimum principle for quadratic spline collocation discretization of a convection-diffusion problem. (English) Zbl 1199.65253
A quadratic spline difference scheme for a one dimensional convection-diffusion problem is derived. The discrete minimum principle is provided by a suitable choice of collocation points. The numerical results imply uniform convergence of order $$O(n^{-2}\ln^2n)$$, where $$n$$ is the number of mesh points.
##### MSC:
 65L10 Numerical solution of boundary value problems involving ordinary differential equations 65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34E15 Singular perturbations, general theory for ordinary differential equations 65L12 Finite difference and finite volume methods for ordinary differential equations