How to discretize the following 4th order PDE using finite difference method?

$$\frac{\partial^{2} y}{\partial t^{2}}+\frac{\partial^{4} y}{\partial x^{4}}=0$$


  • $\begingroup$ Welcome to SciComp.SE! Your question is a bit superficial and in current form, perfectly answered by putting the first sentence into Google. (If not, you should explain that!) What is the background, what about boundary conditions etc.? $\endgroup$ – Christian Clason May 31 '15 at 6:51
  • $\begingroup$ Also, cross-posting is discouraged on the StackExchange network, so people don't waste their time with an answer you already received on the other site. The usual procedure is to wait a few days, and then either raise a flag and ask the moderators for migration (if there are some answers already) or delete the old and ask a new question. $\endgroup$ – Christian Clason May 31 '15 at 6:51
  • $\begingroup$ link: math.stackexchange.com/questions/1306045/… $\endgroup$ – Christian Clason May 31 '15 at 6:52
  • $\begingroup$ this is noted.... im new to this... $\endgroup$ – mich May 31 '15 at 7:03

You can use central difference scheme for both of the time and space derivatives. For time derivative, three time levels would come in to picture i.e. n, n-1 and n+1 where n is the existing time level and n+1 is the one you want to get for the next time step. Use second order accurate space derivative and that would include five grid points ranging from i-2 to i+2. This would be a second order accurate method. Use your boundary conditions and observe that the second and second last point will also need special attention as they can not be calculated with this method. Use B.C. wisely. This surely will do it!

Reference: http://en.wikipedia.org/wiki/Finite_difference_coefficient

  • $\begingroup$ You could improve this answer by including more details, especially the concrete fourth-order stencil. (Ideally, the answer should still be useful after Wikipedia has decided to move this information to a different article.) $\endgroup$ – Christian Clason May 31 '15 at 6:49
  • $\begingroup$ @ChristianClason Thank you for this info. I will take care of this from now on. $\endgroup$ – Tanmay Agrawal May 31 '15 at 6:53
  • $\begingroup$ You could already take care of this now :) (You can always edit your own posts by using the grey "edit" link under your post.) $\endgroup$ – Christian Clason May 31 '15 at 6:54

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