Next: 5. Partial Differential Equations
Up: 4.3 Boundary Value Problems
Previous: 4.3.1 Shooting Method
4.3.2 Relaxation Method
Discretize to transform a given DE
into a set of algebraic equations. For example, applying DDST to
we find
which leads to the set of equations
Since we have a BVP, and will be given.
- Let
be an inaccurate (estimated?)
solution. The error components
together with then define an error vector
.
- How to modify
to make
disappear?
Expand linearly:
This modified error vector is called
. We want it to
vanish,
:
Thus our system of equations is tridiagonal:
Recursion technique!
EXAMPLE:
DDST leads to
. Expand:
Start the downwards recursion:
and
.
brings us down to . Putting
we take the upwards recursion
Improve
and iterate.
Next: 5. Partial Differential Equations
Up: 4.3 Boundary Value Problems
Previous: 4.3.1 Shooting Method
Franz J. Vesely Oct 2005
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001