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# Next steps

There are many texts on PDEs; a fairly popular undergraduate level text is by Haberman {cite}`habermanElementaryApplied1998`.  A more advanced treatment is by
Ockendon *et al*. {cite}`ockendonAppliedPartial2003`.

For a more traditional and analytical take on full discretization of the heat equation, one may consult Smith {cite}`smithNumericalSolution1985` or Morton and Mayers {cite}`mortonNumericalSolution2005`.

Several examples of using the method of lines with spectral method approximation may be found in Trefethen's text {cite}`trefethenSpectralMethods2000`.  A classic text on using spectral methods on the PDEs from fluid mechanics is Canuto *et al.* {cite}`canutoSpectralMethods1988`.  The literature on the complex computational fluid dynamics is vast, but one comprehensive monograph is by Roache {cite}`roacheFundamentalsComputational1998`.

For a first-hand account of the development of numerical methods for equations governing reservoir simulations (close to the heat equation), see the [article by D. W. Peaceman](http://history.siam.org/peaceman.htm), reprinted from {cite}`nashHistoryScientific1990`.  Those were early days in computing!