Naslov
Collocation with High Order Tension Splines

Autori
Beroš, Ivo ; Marušić, Miljenko

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Applied Mathematics and Computation / Rogina, M. ; Hari, V. ; Tutek, Z. - Zagreb, 2001, 91-98

Skup
Conference on Applied MAthematics and Compuation

Mjesto i datum
Dubrovnik, Hrvatska, 13.09.1999. - 17.09.1999

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
tension spline ; collocation method ; boundary value problems

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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