MATLAB: Solve an ODE with runge kutta method

ode15s

Hi,
I'm trying to solve the following eqaution using runge kutta method. I have not seen any examples of ODE45 or ODE15s for equations in this type.
Ay''+Byy'+Cy'+Dy+E=0; where A,B,C,D and E are constants.
Boundary conditions are y(0)=0; y(l)= 2.3
Thanks

Best Answer

Ah, the glory of state-space. First, make the substitution
u = y'
Then, you have a system of two equations
u' = (1/A)*(-B*y*u-C*u-D*y-E)
y' = u
Now you can use ode45...
>> [t,y] = ode45(@xdot,[0 1],[0;0]);
where the function xdot is...
function dx = xdot(t,x)
A = 1;
B = 1;
C = 1;
D = 1;
E = 1;
u = x(1);
y = x(2);
dx(1,1) = (1/A)*(-B*y*u-C*u-D*y-E);
dx(2,1) = y;
Note that I didn't really understand your initial conditions. For your differential equation, you would need to specify an initial y and y', I believe.
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