MATSLISE: (Regular) Sturm-Liouville equation Previous page    Next Page

The (regular) Sturm-Liouville equation

The regular Sturm-Liouville problems (SLP) read

( -p(x)y')'+ q(x)y = Ew(x)y,

where a and b are finite, functions p, q, and w are defined on the closed interval [a,b] with p and w strictly positive. It is also assumed that q is continuous and that p and w can be twice differentiated on the specified interval. The boundary conditions are:

A0*y(a) + B0*p(a)y'(a) = 0
A1*y(b) + B1*p(b)y'(b) = 0

where the constants A0 and B0 are not both zero and similarly for A1 and B1.

Sturm-Liouville problems model phenomena such as the earth's seismic behaviour, the propagation of sonar in water stratified by varying density, the stability and velocity of large-scale waves in the atmosphere,...

Solving the Sturm-Liouville equation with MATSLISE

Figure 3: The problem-specification window for a Sturm-Liouville problem.

Figure 3 shows the problem-specification window for a Sturm-Liouville problem (paine_slp.mat). This window contains the following inputfields:

The user is allowed to enter -inf or inf in the integration-interval-fields: a and b. The integration interval is then chosen by the program and will be wide enough to provide the eigenvalues within the desired tolerance.

Solving SLP means calculating the eigenvalues E and the associated eigenfunctions y. This can be done by clicking the construct-button.


   Regular Schrödinger: The File Menu  The Construct-button