BS Linear Multistep Methods on Non-uniform Meshes

Date of Online Publication: 26/08/2006
Keywords: Boundary Value Problems, Ordinary Differential Equations, B-Splines, Spline Collocation, Boundary Value Methods
Authors: Francesca Mazzia, Alessandra Sestini and Donato Trigiante
Pages: 131-144
BS methods are a special class of Linear Multistep Methods defined using B-spline functions. These methods are always convergent and have good stability properties when used as Boundary Value Methods. In addition, if k is the number of steps, a Ck spline of degree k + 1 can be computed with low computational cost and this serves as a continuous extension to the solution. It is shown that the continuous solution and the discrete solution both share the same order of convergence. In this paper we introduce this class of methods in the general case of a non-uniform mesh and we present numerical results showing their performance when dealing with some singularly perturbed Boundary Value Ordinary Differential Equations.

 

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