solving second order differential equation for 1D wave with parameter by shooting method

Hi I really need help writing a MATLAB code that uses the shooting method to integrate d^2f/dx^2 = -(w^2)*y/180,625 while improving the parameter w by (w_n+1)^2 = (w_n)^2 -f((w_n)^2)/[Delta*f/Delta*w^2 @w_n]. My initial guess is w0=1,570.79645. I'm struggling with turning my second order differential equation into a first order to solve in MATLAB while also integrating with parameter w that improves with each iteration.

[Torsten]

Is y = f ?

What is Delta ? As written, it cancels out in the update of w^2.

Do you have any boundary conditions on f ?

[Gabriela]

@Torsten yes sorry I misstyped f as y so y=f. And f(0)=0 and L=0.75m f(0.75)=0

[Torsten]

You can't have only two boundary conditions (f(0) = f(L) = 0) in a second-order differential equation with an unknown parameter omega . You must have three.

Is this an eigenvalue problem ? Something similar to this example:

https://uk.mathworks.com/help/matlab/math/solve-bvp-with-unknown-parameter.html

?

[Gabriela]

@Torsten I think another boundary condition is f= 425/lamda = w/(2pi) = 277.778n

Answer 1

[Mudit Kumar Bhugari]

Hi @Gabriela

I understand that you want to write MATLAB code for a Second Order Differential Equation using shooting method.

I'm attaching some of the similiar problems which might help you.

• https://in.mathworks.com/matlabcentral/answers/483698-shooting-method-bvp?s_tid=answers_rc1-1_p1_MLT
• https://in.mathworks.com/matlabcentral/answers/52280-using-the-shooting-method?s_tid=answers_rc1-2_p2_MLT
• https://in.mathworks.com/matlabcentral/answers/516859-ode45-shooting-method?s_tid=answers_rc1-3_p3_MLT