specifying the boundary conditions in pdepe

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Hsn Mtl
Hsn Mtl 2013-3-3
评论： ahmed 2018-3-24
Hi, I am trying to solve the PDE of a 1D cantilevered beam using pdepe. The main equation is uxxxx=1/u^3. Since it is a fourth order PDE, I have split it into two second order PDEs as: u1xx=u2 u2xx=1/u1^3 Then I defined the relevant C=[0;0],b=[u1x;u2x],s=[-u2;1/u1^3] My problem is in specifying the boundary conditions which are: For the left end: u1(0)=0 , u1x(0)=0 For the right end: u2(1)=0 u2x(1)=0 I can not input this boundary conditions in the standard form to define matrix p and q. Is there any method to solve this problem?

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回答（1 个）

Bill Greene
Bill Greene 2013-3-3
Hi,
The equation you show is actually an ordinary differential equation with a single dependent variable u and a single independent variable x rather than a partial differential equation.
The function bvp4c can be used to solve a boundary value problem like the one you show. For bvp4c, your 4th order equation has to be converted to 4 first order equations. This note gives a nice example of how to use bvp4c to solve a linear beam equation:
http://www.ce.berkeley.edu/~sanjay/ce130n/2009/lab3.pdf
Extending it to your nonlinear case should be straightforward.
Bill

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