Path: news.mathworks.com!not-for-mail From: <HIDDEN> Newsgroups: comp.soft-sys.matlab Subject: Re: Defining x and y in 2D matrix Date: Mon, 21 May 2012 21:54:06 +0000 (UTC) Organization: The MathWorks, Inc. Lines: 14 Message-ID: <jpedhu$mri$1@newscl01ah.mathworks.com> References: <jpe7b9$phh$1@newscl01ah.mathworks.com> Reply-To: <HIDDEN> NNTP-Posting-Host: www-05-blr.mathworks.com Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: newscl01ah.mathworks.com 1337637246 23410 172.30.248.37 (21 May 2012 21:54:06 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Mon, 21 May 2012 21:54:06 +0000 (UTC) X-Newsreader: MATLAB Central Newsreader 1187260 Xref: news.mathworks.com comp.soft-sys.matlab:768535 "Saud Alkhaldi" wrote in message <jpe7b9$phh$1@newscl01ah.mathworks.com>... > I have a question that's asking me to ise the 4 point central difference to calculate the partial derivatives of the function z=f(x,y). However, I'm only given a set of data in a 100x101 matrix. How can I define my x and y vectors so I can proceed with finding the derivatives. - - - - - - - - - - If you're being asked to use the four point central difference formula to calculate derivatives in a 100 x 101 matrix of z = f(x,y) values, the presumption I would make is that the x and y values correspond linearly to the indices of the matrix. In other words the x-interval between two horizontally adjacent matrix values z(ix,iy) and z(ix+1,iy) is understood to be some constant value h and between two vertically adjacent values z(ix,iy) and z(ix,iy+1) is a constant k in y-difference. That means at each point z(ix,iy) the approximate first partial derivative with respect to x will be given by the four-point central difference using z(ix-2,iy), z(ix-1,iy), z(ix+1,iy) and z(ix+2,iy), and doesn't involve z(ix,iy). It is up to you to decide what h, the x-difference, is to be for the formula. That formula would be: dz/dx(ix,iy) = (z(ix-2,iy)-8*z(ix-1,iy)+8*z(ix+1,iy)-z(ix+2,iy))/(12*h) A similar statement holds for the first partial with respect to y using k and differences in iy. You will note that you cannot apply this formula at the four edges of your matrix since for example you have no values of z for x-indices 0 and -1 or for 101 and 102. You will have to decide to either derive the appropriate third order approximation at the edges or use a cruder difference method there. Roger Stafford