Path: news.mathworks.com!not-for-mail From: <HIDDEN> Newsgroups: comp.soft-sys.matlab Subject: Re: Solving second order differential equations Date: Thu, 25 Nov 2010 23:58:04 +0000 (UTC) Organization: The MathWorks, Inc. Lines: 27 Message-ID: <icmt6c$36s$1@fred.mathworks.com> References: <icm404$2pn$1@fred.mathworks.com> <icm9ap$5nr$1@fred.mathworks.com> <icmmb3$je7$1@fred.mathworks.com> Reply-To: <HIDDEN> NNTP-Posting-Host: webapp-03-blr.mathworks.com Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: fred.mathworks.com 1290729484 3292 172.30.248.38 (25 Nov 2010 23:58:04 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Thu, 25 Nov 2010 23:58:04 +0000 (UTC) X-Newsreader: MATLAB Central Newsreader 1187260 Xref: news.mathworks.com comp.soft-sys.matlab:690103 "Sridatta Pasumarthy" <sridatta1988@gmail.com> wrote in message <icmmb3$je7$1@fred.mathworks.com>... > Hi, > thanks for replying again. > f,g,h are not unknowns. i know the expressions for them. (they stand out for some forms of the electric and magnetic field components of an electromagnetic wave in a waveguide). fifth equation defines w in terms of x' , y' , z'. i don't think the first equation is needed for solving because it is related to the final answer i am supposed to find. i just gave it assuming that it might be of extra help. the principal problem constitutes final four equations. - - - - - - - - If you discard the first equation, then you can express this problem as a system of three second order differential equations in three unknown variables: x'' = (c*g(z) * y') * (1 - x'^2 - y'^2 - z'^2)^2 y'' = (f(z) + g(z) * x' + j(z) * z') * (1 - x'^2 - y'^2 - z'^2)^2 z'' = (c*j(z) * y') * (1 - x'^2 - y'^2 - z'^2)^2 If you wish to solve it numerically for variables x, y, and z, you would express it with six equations. Call p = x', q = y', and r = z'. dp/dt = (c*g(z)*q) * (1-p^2-q^2-r^2)^2 dx/dt = p dq/dt = (f(z)+g(z)*p+j(z)*r) * (1-p^2-q^2-r^2)^2 dy/dt = q dr/dt = (c*j(z)*q) * (1-p^2-q^2-r^2)^2 dz/dt = r See the documentation of the 'ode' functions for the details on this. Notice that the variables x and y never appear in the earlier equations, so if you don't need them specifically, you could simple solve for p, q, and z using only four equations, leaving dx/dt and dy/dt out. I see no particular reason why your original first equation should hold true as to the derivative of w as obtained from the fifth equation unless you were especially lucky in your defined functions, f, g, and j and constant c. Roger Stafford