4th order discretization of 2nd order difference
Does anyone can tell me the form of 4thorder discretization of 2order difference in cylindrical coordinate.
In Cartesian coordinate, it is (F(i2)+16F(i1)30F(i)+16F(i+1)F(i+2))/(12*dx) 
Re: 4th order discretization of 2nd order differen
If you have mathematica/maple/maxima you can find the coefficients using it.Also look for the paper on compact scheme by sanjeev lele ( JCP 1992),it should give you the required finite difference discretization.

Re: 4th order discretization of 2nd order differen
discretization is independent of coordinate system [d2u/dx2 or d2u/dr2 are same]. If, whatever u have wrote, is correct in Cartesian coordinate, it is correct in Cylindrical coordinate as well. So, enjoy!! you already have what r u looking for :)
What changes with change in coordinate system is terms itself, not the way it is discretized. hope it helps. 
Re: 4th order discretization of 2nd order differen
You are right, but I want to discretize the Lapace of Phi in cylindrical coordinate. So the divergence of a gradient in cylindrical is different from the one in Cartetian coordinate.

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