how to find f"(0) where f=y(1),f'=y(2),f"=y(3)

dydx=[y(2);  y(3);  2*a1*y(2)*(y(2)+y(5))-a1*y(3)*(y(1)+y(4));  
      y(5);  y(6);  2*a1*y(5)*(y(2)+y(5))-a1*y(6)*(y(1)+y(4));
      y(8);  A*Pr*a2*y(7)*(y(2)+y(5))-Pr*a2*y(8)*(y(1)+y(4))];

res=[ya(1); ya(2)-1; ya(4); ya(5)-p; ya(7)-1; yb(2); yb(5); yb(7)];

[e-mail]

[Walter Roberson]

Is res your initial conditions?

[MINATI]

yes

Answer 1

[Torsten]

f0 = deval(sol,0);
f0(3)

Best wishes

Torsten.

[MINATI]

Thanks a lot Torsten

yah it works

Answer 2

[Walter Roberson]

%construct initial values any way suitable for you
a1 = rand();
a2 = rand();
A = rand();
Pr = rand();
ya = rand(1,7);
yb = rand(1,7);
p = rand();

%now find the values

dxdy = @(t,y) [y(2);  y(3);  2*a1*y(2)*(y(2)+y(5))-a1*y(3)*(y(1)+y(4));  
    y(5);  y(6);  2*a1*y(5)*(y(2)+y(5))-a1*y(6)*(y(1)+y(4));
    y(8);  A*Pr*a2*y(7)*(y(2)+y(5))-Pr*a2*y(8)*(y(1)+y(4))];
res=[ya(1); ya(2)-1; ya(4); ya(5)-p; ya(7)-1; yb(2); yb(5); yb(7)];
tspan = [0 5];
[t, y] = ode45(dxdy, tspan, res);
f = y(:,1);
f_prime = y(:,2);
f_primeprime = y(:,3);

[MINATI]

Thanks Walter It works