ex15bch1.m

these codes are for solving OED with matlab

function ex15bch1
a = 2;
c = 1;
options = odeset('RelTol',1e-6);
[t,ysol] = ode45(@odes,[0 10],[1; 3],options,a,c);
x = ysol(:,1);
y = ysol(:,2);
G = exp(c*x + a*y) ./ (x.^c .* y.^a);
figure
plot(x,y)
xlabel('x(t)')
ylabel('y(t)')
axis([0 4.5 0 3.5])
title('Solution of Volterra''s predator-prey model.')
figure
plot(t,G)
title('Conserved Quantity G(t,x(t),y(t)).')
%===============================================
function dydt = odes(t,ysol,a,c)
x = ysol(1);
y = ysol(2);
dxdt =  a * (x - x*y);
dydt = -c * (y - x*y);
dydt = [dxdt; dydt];