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4. Ordinary Differential Equations (ODE)
Euler's integration scheme:
respect it, but don't use it!
Find the solution of
(
etc.)
In physics:
- mostly first or second order
- usually given in explicit form, or
Second order DE may be written as 2 DEs of first order:
; .
EXAMPLE:
Harmonic oscillator:
Instead of
, write
or
- If the values of , etc. are all given at :
Initial Value Problem (IVP).
- If , etc. are given at several points
:
Boundary Value Problem (BVP).
Typical IVP: equations of motion
;
and given
Typical BVP: potential equation
;
given at boundary points
Subsections
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Franz J. Vesely Oct 2005
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001