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4.1.6 RungeKutta Method
Figure 4.1:
a) EC formula (= RK of first order);
b) RK of second order

(Also called halfstep method, or EulerRichardson algorithm.)
A much more powerful method that has found wide application is the RK
algorithm of order 4, as described in the table.
Advantages of RK:
 Selfstarting (no preceding needed)
 Adjustable
But:
 Several evaluations of per step; may be too expensive
Stability of RK:
Halfstep + relaxation equation:
.
EXERCISE:
Test various algorithms by applying them to an analytically solvable problem,
as the harmonic oscillator or the 2body Kepler problem. Include in your
code tests that do not rely on the existence of an analytical solution (energy
conservation or such.) Finally, apply the code to more complex problems
such as the anharmonic oscillator or the manybody Kepler problem.
Franz J. Vesely Oct 2005
See also: "Computational Physics  An Introduction," KluwerPlenum 2001