Re: non-linear differential equations.
- To: mathgroup at smc.vnet.net
- Subject: [mg16144] Re: [mg16108] non-linear differential equations.
- From: "Richard Finley" <rfinley at medicine.umsmed.edu>
- Date: Sat, 27 Feb 1999 03:23:10 -0500
- Sender: owner-wri-mathgroup at wolfram.com
Vivek, Do you mean: p - 2^(n-1)(1-beta[z])(1+beta[z]+beta[z]^2)^(n-1) == 1/(Ca r[z]) as your equation implies when rewritten or was it supposed to be p - 2^(n)(1-beta[z])(1+beta[z]+beta[z]^2)^((n-1)/2) == 1/(Ca r[z]) ??? regards, RF >>> <engp7696 at leonis.nus.edu.sg> 02/25/99 07:25AM >>> While using Mathematica I have a problem with the solution of the following non-linear differential equation: p - 2^n (1 + beta[z])(1 + beta[z] + beta[z]^2 )^(n-1)/2 == 1/(Ca r[z] ) where n = is a constant ranging from -infinity to + infinity; p = constant = 2^n (n+2) beta[z] = z r'[z]/r[z] Ca = constant The boundary condition is r[z = 3200] = 10^(-10) I need to obtain a plot of r vs z. The problem is 1)NDSolve seems to be working only when (n-1)/2 is a whole number . i.e for n = 3, 5, 7 etc. 2)NDSolve does not work for n < 3 or when (n-1)/2 is not a whole number 3)Even when NDSolve works for n = 3, 5, 7 etc I also obtain imaginary solutions. This equation has been solved by finite difference methods with no problems using a BASIC code. I would like to know if there is any fool-proof method to solve the problem in Mathematica for all n without obtaining imaginary solutions. @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @ VIVEK PAI UNIVERSITY RESIDENCE Room : E5-03-29 #04-119, Block 224 Chemical Engineering Street 21, Bukit Batok National University of Singapore Singapore 650224 Singapore 119260 Phone : 8971197 Phone : 8742254 email : engp7696 at .nus.edu.sg @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ @