Solve an ODE with runge kutta method

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

Answer 1

[Jarrod Rivituso]

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.

Answer 2

[Jan]

If you have "boundary conditions", you need a different solver, see bvp4c and bvp5c. But two conditions are not enough to find a solution for of 2nd order ODE - you need an additional condition.

[Luke]

I solved this equation with bvp4c. But it takes so long to give me an answer. The people who worked on a similar equation suggested to use a Runge-Kutta Nystrom Method, which I'm not familier. Are you guys conversant with this method?