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

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.

You can low the order by introducing 3 more unknowns, and then solve by Newton method

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.

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.

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.