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188 Polynomial Approximation of Differential Equations
n En n En
2 .8249 × 10 −1 8 .3399 × 10 −7
3 .1814 × 10 −1 9 .2784 × 10 −8
4 .1232 × 10 −2 10 .8594 × 10 −10
5 .1697 × 10 −3 11 .5817 × 10 −11
6 .8560 × 10 −5 12 .1511 × 10 −12
7 .8874 × 10 −6 13 .8770 × 10 −14
Table 9.2.1 - Errors relative to the Legendre collocation
approximation of problem (9.1.3).
We consider another example. In figure 9.2.1, we plot the approximating polynomials
pn, n = 4, 10, 16, obtained by the collocation method (9.2.7) at the Legendre nodes.
Figure 9.2.1 - Legendre collocation approximations for n = 4, 10, 16.