PDE and ODE couple system solving

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Danila Zharenkov
Danila Zharenkov on 19 May 2013
Hello, I have to solve the following system https://dl.dropboxusercontent.com/u/12616416/system.jpg But I don't know what to do with integral and how to solve such type of system. The system can't be solved for s->infinity, so I uses s->10. I tried to solve this system without integral using pdepe function
%PDE and ODE system
function [ a,b,c ] = eqn1( s,t,u,DuDs )
alpha=0.001;
m=0.08;
b=20;
q=0.02;
a=[1; 1];
b=[0; 1e-6] .*DuDs;
c=[b-u(1)-q*u(1); alpha*s*u(1)*u(2)-m*u(2)];
end
% initial conditions
function u0 = initial1(s)
switch s
case (s>=0.9975 & s<1)
value=8*(s-0.9975);
case (s>=1 & s<1.005)
value=0.02;
case (s>=1.005& s<=1.0075)
value=8*(1.0075-s);
otherwise
value=0;
end
u0=[1000; value];
end
%boundary conditions
function [ pl,ql,pr,qr ] = bc1( sl,ul,sr,ur,t )
pl=0;
ql=1;
pr=ur;
qr=10;
end
But matlab writes, that boundary conditions for first equation are nessesary. Can you please give me some advice for this problem? Thanks.
  1 Comment
Danila Zharenkov
Danila Zharenkov on 19 May 2013
I tried to modify boundary conditions like this
pl=vl;
ql=[0,1];
pr=vr;
qr=[0,10];
Is this the right way?

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