ex7b.m

fokker-planck example

dt=1;

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

k1=0.1;
s1=1;

b=0.01;

for i=1:100
  t(i)=i;
end  


for j=1:100  

  r=randn(100,1);

  w0=0;
  for i=2:100
    w(i)=w(i-1)+sqrt(dt)*r(i);
  end  

  %the numerical solution of the BOD model with the Euler scheme
  x0=20.0;
  x(1)=x0-k1*x0*dt+s1*dt+0.5*x0*b*dt-x0*b*sqrt(dt)*r(1);
  for i=2:100
    x(i)=x(i-1)-k1*x(i-1)*dt+s1*dt+0.5*x(i-1)*b*dt-x0*b*sqrt(dt)*r(i);
  end  

  mean=mean+x;
  
  var=var+x.*x;
  
end 

mean=mean/100;

rms=sqrt(var/100-mean.*mean);

plot(t,mean,'-',t,rms,'- ');
 
title('Mean and Standard Dev. of 100 BOD Realizations - Stratonovitch')
xlabel('Distance')
ylabel('Mean and Std. Dev.')
legend('Mean','Std. Dev.',0)