This worksheet contains all the examples from the paper

S. Cyganowski, L. Gruene and P.E. Kloeden: MAPLE for Stochastic Differential Equations

(in: J.F. Blowey, J.P. Coleman, A.W. Craig, eds., Theory and Numerics of Differential Equations, Springer Verlag(2001), 127-178)

which can be obtained from http://www.math.uni-frankfurt.de/~numerik/kloeden/maplesde/ .

It assumes that you have installed the stochastic package, which can be downloaded from the above link.

For an explanation of the examples please consult the above paper.

Last Changed June 21, 2005 by Lars Gruene (http://www.uni-bayreuth.de/departments/math/~lgruene/)

restart;

read `stochastic9`;

with(stochastic);

L0(x[2],[x[1],x[2]],[[r,u],[s,v]]);

LJ(x[2],[[r,u],[s,v]],2);

LJ(x[2],[[r,u],[s,v]],1);

MLJ(x[2],[x[2],x[1]],[[r,u],[s,v]],2);

MLJ(x[2],[x[2],x[1]],[[r,u],[s,v]],0);

itoformula([(x[1])^2],[a*x[1]],[[b*x[1]]]);

LFP(p(s,x,t,y[1]),[a],[[b]]);

p:=(s,x,t,y)->1/(sqrt(2*pi*b^2*(t-s)))*exp(-(y-x-a*(t-s))^2/(2*b^2*(t-s)));

LFP(p(s,x,t,y[1]),[a],[[b]]);

simplify(%);

correct([x[1],x[2]],[[r,0],[0,r]],2);

correct([x[1],x[2]],[[x[1],0],[0,r]],1);

conv([-a^2*x[1]*(1-x[1]^2)],[[a*(1-x[1]^2)]],ito);

conv([0],[[a*(1-x[1]^2)]],strat);

SL0(x[2],[x[1],x[2]],[[r,u],[s,v]]);

chainrule([(x[1])^2],[a*x[1]],[[b*x[1]]]);

linearsde(-x,2);

reducible(x^3,x^2);

explicit(1/2*a^2*x,a*x);

linearize([x[2],-b*x[2]-sin(x[1])-c*sin(2*x[1])],[[0],[-a*(x[2])^2+sin(x[1])]],[0,0]);

A:=array(1..2,1..2,[[2,2],[1,1]]);

A := matrix([[2, 2], [1, 1]]);

B1:=array(1..2,1..2,[[3,1],[4,2]]);

B:=[B1];

sphere(A,B);

q0;

print(qk);

print(h);

print(hk);

A:=array(1..2,1..2,[[a11,a12],[a21,a22]]);

B:=array(1..2,1..2,[[b11,b12],[b21,b22]]);

E:=[B];

momenteqn(A,E);

P:=array(1..5,1..5,[[2,5,10,17,26],[5,6,11,18,27],[10,11,12,19,28],[17,18,19,20,29],[26,27,28,29,30]]);

pmatrix2pvector(P);

P:=[[1,2],[2,4]];

pmatrix2pvector(P);

p:=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15];

pvector2pmatrix(p);

comm1([1,0],[0,x[1]]);

comm2([1,0],[(x[2])^2*(x[1])^4,(x[1])^2]);

colour([a(x[1],t)],[b(x[1],t)]);

colour([x[2],x[1]*(alpha-x[1]^2)-x[2]],[0,sigma*x[1]]);

Euler([x[2],x[1]],[[r,u],[s,v*x[1]]]);

Milstein([x[2],x[1]],[[r,u],[s,v*x[1]]]);

comm1([b*x[1],c*x[1]]);

milcomm([a*x[1]], [[b*x[1],c*x[1]]]);

Taylor1hlf([x[2],x[1]],[[r,u],[s,v]]);

Taylor2([x[2],x[1]],[[r,u],[s,v]]);

wkeuler([x[1],x[2]],[[r,u],[s,v]]);

wktay2([x[1],x[2]],[[r,u],[s,v]]);

wktay3([x[2],x[1]],[[r,u],[s,v]]);