Next: 4.3.1 Shooting Method
Up: 4. Ordinary Differential Equations
Previous: 4.2.6 Numerov's Method
4.3 Boundary Value Problems
Examples:
- Poisson's and Laplace's equations,
, or
where is a charge density. (Laplace:
).
Another physical problem described by the same equation is the temperature
distribution along a thin rod:
.
- Time independent Schroedinger equation for a particle of mass
in a potential :
The general 1-dimensional BVP reads
with boundary values required. Typically there are
boundary values
at , and
boundary values
at .
The quantities and may simply be higher derivatives
of a single solution function .
Two methods are available:
- Shooting method
- Relaxation technique
Subsections
Next: 4.3.1 Shooting Method
Up: 4. Ordinary Differential Equations
Previous: 4.2.6 Numerov's Method
Franz J. Vesely Oct 2005
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001