Re: Question: numerical solution of nonlinear differential equation
- To: mathgroup at smc.vnet.net
- Subject: [mg26397] Re: Question: numerical solution of nonlinear differential equation
- From: Alexandra Milik <amilik1 at compuserve.com>
- Date: Wed, 20 Dec 2000 00:21:25 -0500 (EST)
- References: <91f7n8$556@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi Ronald, your boundary value problem has no solution, to see this let z = Exp[-Dx] y' = w which yields the linear system of first order differential equations w' = B/A w -C/A z z' = -D z y' = w with boundary values w(0) = w(E) =0. The third equation decouples so we are left with a planar linear system of the form u'=Ju with u=[w z] and matrix [ B/A -C/A ] J= | | [ 0 -D ] of which the eigenvalus are B/A and -D, this implies that the trivial solution w=z=0 is a saddle for positive B/A and D and a node otherwise. In case of the node all solutions are lines through the origin of the (wz)-plane, in case of the saddle there are two lines through the origin and hyperbolas in between. None of this solutions crosses the z-achses twice. Thus there exists no solution to your BVP. Hope this helps Alex Ronald Sastrawan schrieb: > Hello ! > > I encountered a problem, trying to numerically solve a differential > equation. > My equation looks like: > > A y''[x] - B y[x]' + C Exp[-Dx] == 0 > with boundary conditions: y'[0]==0 , y'[E]==0 > > All constants A to E are known. > > Mathematica complains, that the equation is not linear. But in the > online documentation I saw many examples of nonlinear differential > equations, which all work fine. What is the difference between the > examples and my equation ? And is there a possibility to NDSolve my > equation ? > > Any hint on this would be of great help to me. > > Thanks a lot, > > Ronald > > -- > Ronald Sastrawan > > Freiburg Materials Research Center > Stefan-Meier-Str. 21 > D-79104 Freiburg > Germany > Tel: ++49/761/203-4802 > FAX: ++49/761/203-4801 > EMAIL: sastra at fmf.uni-freiburg.de > http://www.fmf.uni-freiburg.de/~biomed/FSZ/forschung-FSZ.html