Convergence of a finite difference approximation

Martin Reavy — Sat, 07 Nov 2009 13:01:04 -0500

As part of the coursework for one of my university courses, I've been asked to find the roots of a finite difference approximation of pressure across a Michell bearing section (ie. find peak pressure). Matlab isn't taught as part of this course (or any of my others for that matter), but is taken as assumed knowledge. Naturally I'm stumped. I've simplified my f.d.a down to:

Pn = (Pn+1 + Pn-1)/2 + [3C(Pn+1 - Pn-1)]/[800(h + xC)] + K/[4(h + xC)^3]

where C, h and K are constants, with 0<x<0.1 along 21 grid points (including the zero).

As far as I understand, I need a code which calculates Pn for each value of x, with initial values of P0 and P21 equal to zero, which takes the previous value of Pn and uses it as Pn-1. The first time round, Pn+1 will be assumed zero, but for the second round of iterations it will use the values calculated from the previous round, and this will continue until the solution has converged. As such, I'll need to store the calculated values of Pn in an array, to be used in the next round of calculations. Once the solution has converged, I need to use Matlab to plot a graph of pressure distribution, and state the number of iterations needed for convergence. Having never used Matlab, I don't have the blindest idea how to do this, although I'm assured by the lecturer that it's a fairly simple piece of code(!).

As this is for a university assignment, I DON'T want someone to produce a nice working code for me, but rather a list of the commands needed to solve the problem, and a short summary of how to use them. Hopefully someone understands my description and can help me out.

Thanks.

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Convergence of a finite difference approximation