72.1 Functions and Variables for lindstedt

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").

Categories: Differential equations · Share packages · Package lindstedt ·