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partial-differential-equations

From boundary conditions to a Sturm-Liouville eigenvalue problem

taught

Substitute a separated PDE's own boundary conditions into the X(x) equation to produce a regular Sturm-Liouville eigenvalue problem, pinning down which separation-constant values are allowed.

Taught in

Requires

Required by

Local knowledge map

Local knowledge map

Choosing which series a boundary-condition pair calls for Comparing the heat and wave equations Finite differences for the heat equation: the explicit scheme Heat conduction in two and three dimensions Long-time behavior and steady-state limits of a separated solution Shifting nonhomogeneous boundary data to… Solving the heat equation with a source term by eigenfunction… Solving the heat equation on a finite rod with Dirichlet… From boundary conditions to a Sturm-Liouville… Fourier sine series Laplace's equation by separation of variables on a disk Laplace's equation by separation of variables on a… Orthogonality of Sturm-Liouville eigenfunctions Singular Sturm-Liouville problems, previewed Solving the heat equation on a finite rod with Neumann… Solving the heat equation on a finite rod with Robin… Solving the vibrating-string problem by separation… The regular Sturm-Liouville problem The separation-of-variables ansatz Boundary-value problems, contrasted with IVPs Eigenvalues and the characteristic equation The linear differential operator L

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