Application of Tension Splines to Singularly-Perturbed Boundary Value Problems for ODE
by
Miljenko Marusic
Department of Mathematics, U. of Zagreb

Besides applications in the shape preserving approximations, tension splines also found their role in the numerical solutions of the boundary value problems for the ODE. We consider problem of the form \epsilony''+ py'+ qy = f. It is known that classical polynomial methods fail when perturbation parameter \epsilon is small. Reason for this is exponential behaviour of the solution on the boundary layer. Using tension splines, i.e., functions that are piecewise combination of linear (polynomial) and hyperbolic functions, we obtain method that approximates solution well, even in the case when perturbation parameter is small.

Here we present different collocation methods for numerical solution of singularly perturbed BVP for ODE. Theoretical and computational aspects of presented methods will be discussed. Especially, some improvements of existing methods will be pointed out, as well as possible applications to some other similar problems.

Date received: March 15, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caex-14.