Abstract
Shooting methods are a popular way of solving Sturm-Liouville problems. Codes in common use, such as SLEIGN and the NAG routine D02KDF, employ general-purpose integrators of fixed, relatively low order for shooting and make decisions using estimates of the global (true) error. In this paper a specialized integrator based on global extrapolation is proposed. Global extrapolation provides a convenient means of adapting the order to the problem and of using very high order when appropriate. It automatically provides a reliable global error estimate. An extremely efficient use is made of evaluations of the coefficients
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