# Nonlinear PDE

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 December 18, 2002, 07:40 Nonlinear PDE #1 eyesfront Guest   Posts: n/a 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

 December 18, 2002, 09:22 Re: Nonlinear PDE #2 Praveen Guest   Posts: n/a 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.

 December 18, 2002, 14:35 Re: Nonlinear PDE #3 xueying Guest   Posts: n/a You can low the order by introducing 3 more unknowns, and then solve by Newton method

 December 19, 2002, 05:11 Nonlinear PDE in more detail #4 eyesfront Guest   Posts: n/a 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.

 December 19, 2002, 05:12 Re: Nonlinear PDE #5 versi Guest   Posts: n/a 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.

 December 19, 2002, 16:20 Re: Nonlinear PDE #6 Dr Strangelove Guest   Posts: n/a 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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