ISSN:
0945-3245
Keywords:
AMS(MOS): 65L05
;
65L07
;
65D07
;
65D10
;
41A15
;
CR: G.1.7
;
G.1.2
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary In this paper non-linear splines (depending onn+1 parameters) are used to patch up the solution of an initial value problem in intervals of stepsizeh. The elements of the solution are fixed byq smoothness conditions andd conditions derived from the differential equation in an appropriate setup. The feasibility of the method can be connected to that of the polynomial spline method by a perturbation type argument. Thus the question of convergence forh→0 is closely connected to the linear (polynomial) case. A new elementary prove is given for divergence of the polynomial splines ifq is larger thand+1, as was done by Mülthei [4] with other techniques. A byproduct is an extention of the famous result for polynomial interpolation by Runge on equidistant grids that interpolation of a given function by splines of too high smoothness can cause divergence forh→0.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01389478
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