New Approach for Constructing Shape-Preserving Hyperbolic and Thin Plate Splines
by
Boris I. Kvasov
Suranaree University of Technology

We define shape-preserving splines as the solutions of differential multipoint boundary value problem (DMBVP for short). For the numerical treatment of DMBVP we replace the differential operator by its difference approximation. This permits us to avoid calculating hyperbolic functions and to easily find mesh solution. We consider the basic computational aspects of this approach and illustrate its main advantages by the examples of hyperbolic tension splines and generalized thin plate splines.

Date received: November 20, 2001