Abstract :
In recent years several high quality Sturm–Liouville software packages have been written (e.g., SLEDGE, SLEIGN, the NAG routine SL02FM). All excel at providing eigenfunction estimates at a finite set of points but only the NAG routine provides interpolation capability, and this by a fairly crude method (especially when compared with the sophistication of its eigenvalue solver). We describe an accurate, efficient method of approximating Sturm–Liouville eigenfunctions based on a small sample of given accurate values. Even though the theory is developed only for regular problems, the algorithm can be extended to many singular cases.
