How to solve a fourth order differential equation (boundary value problem) with constraint?
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Hi everyone, I was trying to solve the following fourth order differential equation: A·x-B·x·w''''(x)=w(x) where A and B are constants,and 0<x<l, and the boundary conditions are w(0) = 0, w'(0) = 0, w''(l)=0, w'''(l)=0. I solved the equation with bvp4c. Now I want to add constraint to w''''(x), i.e., 0<w''''(x)<C, where C is a constant. How can I add this constraint? Thanks, JZ
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Torsten
2024년 6월 4일
편집: Torsten
2024년 6월 4일
And as far as I see, a necessary and sufficient condition that w'''' is bounded on [0 l] is w(0) = 0, and that's what you already postulate as boundary condition for your problem.
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Torsten
2024년 6월 5일
There is no way to impose an additional constraint apart from the 4 boundary conditions. If the solution of the differential equation you get does not satisfy your constraint and you think it should, then either the differential equation is wrong or implemented with errors or it has more than one solution.
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