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Old   December 18, 2002, 07:40
Default Nonlinear PDE
  #1
eyesfront
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Dear all, how to solve a nonlinear PDE which is fourth order in space(one dimension r in cylindrical coordinate) and first order in time. I have got the initial configuration, four other boundary conditons.

Thanks in advance
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Old   December 18, 2002, 09:22
Default Re: Nonlinear PDE
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Praveen
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There are no general methods for the solution of pde. You will have to give complete details of the problem, pde, ic, bc, and geometry before anybody can help you.
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Old   December 18, 2002, 14:35
Default Re: Nonlinear PDE
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xueying
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You can low the order by introducing 3 more unknowns, and then solve by Newton method
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Old   December 19, 2002, 05:11
Default Nonlinear PDE in more detail
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eyesfront
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Thanks for your reply. The PDE is like the following

-dh/dt=h^3*(1/r^3*dh/dr-1/r^2*d^2h/dr^2+2/r*d^3h/dr^3+d^4h/dr^4+h^2*dh/dt(-1/r^2*dh/dr+1/r*d^2/dr^2+d^3/dr^3)

at t=0, initial configuraton h(r) given at r=0, dh/dr=0 and d^3h/dr^3 =0 at r=2, dh/dr=1 and d^2/dr^2=1

It seems impossilbe to lower the order of derivatives by introducing three other unknown since this is a nonlinear PDE.

I look forward to your further comments.

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Old   December 19, 2002, 05:12
Default Re: Nonlinear PDE
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versi
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If it looks like a diffusion ( 4th order dissipation) , it can be solved by implicit schemes such as backward Euler and a central scheme for spatial 4th order terms.
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Old   December 19, 2002, 16:20
Default Re: Nonlinear PDE
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Dr Strangelove
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If you've got an initial condition that is sufficiently differentiable, then you can march forward in time pretty easily, even using something as simple as Backward Euler.

Many books on numerical methods and on CFD can provide you with more details on methods that will probably work with your equation.
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