# Numerical solution of singular perturbed boundary value problems using a collocation method with tension splines

• Maximilian R. Maier
Chapter
Part of the Progress in Scientific Computing book series (PSC, volume 5)

## Abstract

A collocation method is given for the numerical solution of a singular perturbed boundary value problem of the form:
$$\begin{gathered} y' = f\left( {x,y,\varepsilon } \right){\kern 1pt} a \leqslant x \leqslant b \hfill \\ r\left( {y\left( a \right),y\left( b \right)} \right) = 0 \hfill \\ y = {\left( {{y_1}, \ldots ,{y_n}} \right)^t}{\kern 1pt} {y_i}:\left[ {a,b} \right] \to R \hfill \\ f = {\left( {{f_1}, \ldots ,{f_n}} \right)^t}{\kern 1pt} {f_i}:\left[ {a,b} \right] \to R \hfill \\ r = {\left( {{r_1}, \ldots ,{r_n}} \right)^t}{\kern 1pt} {r_i}:R \times R \to R \hfill \\ \end{gathered}$$
(1.1)

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