Collocation by Higher Order Tension Splines
by
Ivo Beroš
Departments of Mathematics, University of Zagreb
Coauthors: Miljenko Marušić (Department of Mathematics, University of Zagreb)

Tension spline of order k is a function that, for given partition x₀ < x₁ < ... < x_n, on each interval [x_i, x_i+1] satisfies differential equation (D^k-p_i²/h_i² D^k-2)u=0, where p_i's are prescribed nonnegative real numbers.

Many articles deal with tension splines of order four applied to collocation method for solving singularly perturbed boundary value problem

(Lu)(x)=\epsilonu''(x)+b(x) u'(x)+c(x)u(x)=f(x),     (0 <= x <= 1)

with boundary conditions

u(0)=u0,     u(1)=u1 .

Accuracy of considered approximations is O (h) or O (h²) for small perturbation parameter \epsilon, depending on the choice of collocation points.

Here we present an algorithm for a collocation method with high order tension splines.

Our objective is to obtain approximation of the higher order of accuracy for the solution of singularly perturbed differential equation. Proof of convergence for some class of tension splines will be presented.

Date received: March 13, 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 # cadz-72.