(maxima.info)Functions and Variables for lindstedt
68.1 Functions and Variables for lindstedt
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-- Function: Lindstedt (<eq>,<pvar>,<torder>,<ic>)
This is a first pass at a Lindstedt code. It can solve problems
with initial conditions entered, which can be arbitrary constants,
(just not <%k1> and <%k2>) where the initial conditions on the
perturbation equations are z[i]=0, z'[i]=0 for i>0. <ic> is the
list of initial conditions.
Problems occur when initial conditions are not given, as the
constants in the perturbation equations are the same as the zero
order equation solution. Also, problems occur when the initial
conditions for the perturbation equations are not z[i]=0, z'[i]=0
for i>0, such as the Van der Pol equation.
Example:
(%i1) load("makeOrders")$
(%i2) load("lindstedt")$
(%i3) Lindstedt('diff(x,t,2)+x-(e*x^3)/6,e,2,[1,0]);
2
e (cos(5 T) - 24 cos(3 T) + 23 cos(T))
(%o3) [[[---------------------------------------
36864
e (cos(3 T) - cos(T))
- --------------------- + cos(T)],
192
2
7 e e
T = (- ---- - -- + 1) t]]
3072 16
To use this function write first 'load("makeOrders")' and
'load("lindstedt")'.
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