# 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)

## Keywords

Boundary Layer Collocation Method Space Charge Region Tension Parameter Boundary Layer Type
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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