Re: non-linear boundary value problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg30284] Re: non-linear boundary value problem*From*: bghiggins at ucdavis.edu (Brian Higgins)*Date*: Sat, 4 Aug 2001 20:02:11 -0400 (EDT)*References*: <9kg1h0$ii8$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Richard, Here is one method based on a shooting technique. Consider the following BVP: y''[x]+Sin[y[x]]=Cos[5x] y[-1]=0,y[1]=0 Note the eqns are nonlinear due to the Sin[y[x]] term. Write the above as two first order ODEs by letting y1[x]=y[x] y1'[x]=y2[x] y2'[x]=-Sin[y1[x]]+Cos[x] with initial conditions y1[-1]=0,y2[-1]=a Here the parameter a is the unknown "initial condition" we want to find such that y1[1]=0. The following code implements the shooting technique system[a_] := {y1'[x] == y2[x], y2'[x] == -Sin[y2[x]] + Cos[5x], y1[-1] == 0, y2[-1] == a}; myODEsoln[a_] := NDSolve[system[a], {y1[x], y2[x]}, {x, -1, 1}] yend[a_] := (y1[x] /. myODEsoln[a]) /. x -> 1 bc = FindRoot[First[yend[a]] == 0, {a, -2, 2}]; Plot[Evaluate[y1[x] /. myODEsoln[a /. bc]], {x, -1, 1}, AxesLabel -> {"x", "y1(x)"}]; This method can be used to solve higher order systems with a variety of BCs. The key is to determine good guesses for the FindRoot algorithm. If the equations are very stiff, then it is advisible to plot the solution as a function of a to get some idea how the solution behaves before attempting a Findroot calculation. Have fun Cheers, Brian Richard S Hsu <rhsu at U.Arizona.EDU> wrote in message news:<9kg1h0$ii8$1 at smc.vnet.net>... > Hi, I am sorry that I asked a wrong question before. > The question should be > Where I could find a mathematica program to solve > a non-linear boundary value problem : > > f''[ x ] == g[ f[x] ], f[0] == a, f'[L] == b , > > where g is a known function, a,b and L are constants. > > The NDSolve does not work for non-linear problems. > > Thanks.