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

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Gabriela 2023-6-29

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https://ww2.mathworks.cn/matlabcentral/answers/1989478-solving-second-order-differential-equation-for-1d-wave-with-parameter-by-shooting-method

评论： Gabriela 2023-6-29

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.

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Torsten 2023-6-29

编辑：Torsten 2023-6-29

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