ex6.m

fokker-planck example

dt=.1;
b=0.2;
randn('seed',717171)

r=randn(100,1);

t=zeros(100,1);
w=zeros(100,1);

w0=0;

t(1)=1;
w(1)=w0;

for i=2:100
  t(i)=i;
  w(i)=w(i-1)+sqrt(dt)*r(i);
end  


%the exact solution
ew=exp(b*w); 

 
%the numerical solution with the Euler scheme
x0=1.0;
x(1)=x0;
for i=2:100
  x(i)=x(i-1)+0.5*b*b*x(i-1)*dt+x(i-1)*b*sqrt(dt)*r(i);
end  

 
plot(t,ew,'-',t,x,'.-');
title('Exact Solution and Euler Numerical Solution')
xlabel('time t')
ylabel('X(t)')
legend('Exact','Numerical',0)