4.7 note p5 added 2/15/17 animation figure 9.5 in text page 434


Animation of figure 9.5 in text page 434, compare higher order boundary layer solutions

This is an animation of the percentage error between boundary layer solution and the exact solution for \(\epsilon y''+(1+x)y'+y=0\) for different orders. Orders are given in text up \(y0,y1,y2,y3\). We see the error is smaller when the order increases as what one would expect.

The percentage error is largest around \(x=0.1\) than other regions. Why? Location of matching is between \(y_{in}\) and \(y_{out}\). Due to approximation made when doing matching? But all boundary layer solutions underestimate the exact solution since error is negative.

The red color is the most accurate. 3rd order.

First animation


second animation


third animation