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Collocation with High Order Tension Splines (CROSBI ID 483499)

Prilog sa skupa u zborniku | izvorni znanstveni rad | međunarodna recenzija

Beroš, Ivo ; Marušić, Miljenko Collocation with High Order Tension Splines // Applied Mathematics and Computation / Rogina, M. ; Hari, V. ; Tutek, Z. (ur.). Zagreb, 2001. str. 91-98

Podaci o odgovornosti

Beroš, Ivo ; Marušić, Miljenko

engleski

Collocation with High Order Tension Splines

Tension spline of order $k$ is a function that, for a given partition $x_0 < \cdots < x_n$, on each interval $[x_i, x_{;i + 1};]$, satisfies differential equation $(D^k - (p_i^2 / h_i^2) D^{;k - 2};) u = 0$, where $p_i$'s are prescribed nonnegative real numbers. Many articles deal with tension splines of order four applied to collocation methods for solving singularly perturbed boundary value problem \begin{;displaymath}; \displaylines{; \hfill ({;\cal{;L};};u)(x) = \varepsilon u''(x) + b(x) u'(x) + c(x) u(x) = f(x), \quad 0 \leq x \leq 1, \hfill \cr \noalign{;\hbox{;with boundary conditions};}; \hfill u(0) = u_0, \quad u(1) = u_1. \hfill \cr}; \end{;displaymath}; Accuracy of considered approximations is ${;\cal O};(h)$ or ${;\cal O};(h^2)$ for small perturbation parameter $\varepsilon$, 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 approximations of higher order of accuracy for the solution of singularly perturbed differential equation.

tension spline ; collocation method ; boundary value problems

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Podaci o prilogu

91-98.

2001.

objavljeno

Podaci o matičnoj publikaciji

Applied Mathematics and Computation

Rogina, M. ; Hari, V. ; Tutek, Z.

Zagreb:

Podaci o skupu

Nepoznat skup

predavanje

29.02.1904-29.02.2096

Povezanost rada

Matematika