A SMALL EXAMPLE FOR THE USE OF "STOCHPLOT9" FOR MAPLE 9

CALLING SEQUENCE: stochplot(s,t,p,z) stochplot plots a numerical solution using one of the schemes from the stochastic package for 1d SDEs

INPUT: s: numerical scheme (as provided by the output of the "Euler", "Milstein" etc. Routines from the stochastic Package)

h: time-step p: number of steps to compute z: initial value

restart;

read stochastic9;

read stochplot9;

with(stochastic);

Construction of the Numerical Scheme...

Euler([-(a*sin(x[1])+2*b*sin(2*x[1]))],[[sigma]]);

Euler([-(1*sin(x[1])+2*2*sin(2*x[1]))],[[0.5]]);

...and output of a point-trajectory using "stochplot"

stochplot(Euler([-(1*sin(x[1])+2*2*sin(2*x[1]))],[[0.5]]), 0.1, 10, 1);

Smaller time step and more steps

stochplot(Euler([-(1*sin(x[1])+2*2*sin(2*x[1]))],[[0.5]]), 0.01, 100, 1);

Same times but different initial value

stochplot(Euler([-(1*sin(x[1])+2*2*sin(2*x[1]))],[[0.5]]), 0.01, 100, 10);

Other schemes can be used the same way:

milcomm([-(1*sin(x[1])+2*2*sin(2*x[1]))],[[0.5]]);

stochplot(milcomm([-(1*sin(x[1])+2*2*sin(2*x[1]))],[[0.5]]), 0.01, 100, 1);

For time dependent SDEs you can use "stochplot_time":

CALLING SEQUENCE: stochplot_time(x,t,p,z) stochplot_time plots a numerical solution using one of the schemes from the stochastic package for 1d SDEs which may be

time dependent, where time in the SDE should be written as "t" INPUT: s: numerical scheme (as provided by the output of the "Euler", "Milstein" etc. Routines from the stochastic Package)

h: time-step p: number of steps to compute z: initial value

t0: initial time

An Example:

stochplot_time(Euler([-(t*sin(x[1])+2*2*sin(2*x[1]))],[[0.5]]), 0.01, 100, 10, 1);