Solving a non-linear second order ODE with Matlab

I am brand new to Matlab, but I have to find an approximate numerical solution to the following differential equation:

d^2p/dr^2+dp/dr*1/r-2*exp(m(r))*sinh(p)=0 OR p''+p'*(1/r)-2*exp(m(r))*sinh(p)=0

I have separated it (I think correctly??) into two first order ODEs:

y0'=y1 y1'=2*exp(m(r))*sinh(y1)

Now I am confused on how to input this into Matlab. Any help is greatly appreciated!

Answer 1

[Torsten]

Use UDE45 if your problem is an initial value Problem, use bvp4c if it is a boundary value problem.

Best wishes

Torsten.

[Torsten]

Sorry, should read ODE45 instead of UDE45.

Best wishes

Torsten.

[Torsten]

And your system of equations must read

y0'=y1
y1'=-y1/r+2*exp(m(r))*sinh(y0)

Best wishes

Torsten.

[Jan]

@Torsten: You know that you can edit your messages?

Answer 2

[Pratik Bajaria]

Hello,

ode45 must work for you. All you have to do is make a function handle, which carries your ode function that you have split into set of first order differential equations and then use ode45 solver in MATLAB to attain a solution.

Similar to example shown on this URL: ODE45

Hope it helps!

Regards, Pratik

Answer 3

[Bjorn Gustavsson]

Another pointer...

You have in fact not separated your DE correctly. You get y1' directly from your DE if you change dp/dr with y1.

HTH