Transcription of Sturm–Liouville Problems
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Sturm–Liouville Problems
sturm liouville ProblemsMore general eigenvalue problemsSo far all of our example PDEs have led to separated equationsof the formX + 2X= 0, with standard Dirichlet or Neumann boundary conditions. Notsurprisingly, more complicated equations often come up in practical Problems . Forexample, if the medium in a heat or wave problem is spatially inhomogeneous,* therelevant equation may look likeX V(x)X= 2 Xfor some functionV, or evena(x)X +b(x)X +c(x)X= , if the boundary in a problem is a circle, cylinder, or sphere, the solution of theproblem is simplified by converting to polar, cylindrical, or spherical coordinates,so that the boundary is a surface of constant radial coordinate.
Sturm–Liouville Problems More generaleigenvalue problems So far all of our example PDEs have led to separated equations of the form X′′ + ω2X = 0, with standard Dirichlet or Neumann boundary conditions.Not surprisingly, more complicated equations often come up in practical problems.
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