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# Next steps

A text a bit above the level of this text is by Ascher and Petzold {cite}`ascherComputerMethods1998`, which covers shooting and finite-difference collocation methods for linear and nonlinear BVPs, with a number of theoretical and applications problems.  A graduate-level text solely on numerical solution of BVPs is by Ascher, Mattheij, and Russell {cite}`ascherNumericalSolution1995`. Besides the shooting and finite-difference methods, it briefly discusses Galerkin and spline-based methods, and it goes into more depth on theoretical issues.  A more detailed treatment of the Galerkin method can be found in Quarteroni, Sacco, and Saleri {cite}`quarteroniNumericalMathematics2007`.  An older and accessible treatment of Galerkin and finite element methods can be found in Strang and Fix {cite}`strangAnalysisFinite1997`.

For spectral methods, an introduction to BVPs may be found in Trefethen's book {cite}`trefethenSpectralMethods2000`, and a more theoretical take is in Quarteroni *et al.* {cite}`quarteroniNumericalMathematics2007`.

In this chapter, a number of linear variable-coefficient BVPs for so-called special functions were mentioned: Bessel's equation, Laguerre's equation, etc.  These ODEs and their solutions arise in the solution of partial differential equations of mathematical physics, and were extensively characterized before prior to wide use of computers {cite}`abramowitzHandbookMathematical2013`.  These special functions have come to be used for many things and are now available at https://dlmf.nist.gov {cite}`olverNISTHandbook2010`.