Re: shooting method, boundary value problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg113775] Re: shooting method, boundary value problem*From*: Alois Steindl <Alois.Steindl at tuwien.ac.at>*Date*: Fri, 12 Nov 2010 05:26:43 -0500 (EST)*References*: <ibgitq$e87$1@smc.vnet.net>

Hello, as stated, your problem has really only the trivial solution. But if you replace the second boundary condition by y(Pi/2)=0, you get a whole family of solutions y=A Cos[t]. In order to pick one of these, you could replace the second boundary condition by a proper initial condition, say y[0]=A. The second boundary condition would still be satisfied. If you are thinking about nonlinear problems, the period of the solution could vary. To state the problem as a standard BVP, you have to rescale your x variable, e.g. by setting x = T*tau, where T satisfies the trivial ODE T'=0. tau is the rescaled time. So you could also specify your problem as y''[tau]+T[tau]^2 y[tau] ==0, T'[tau]==0, y[0]==A, y'[0]==0, y[1]==0 with the initial guess T[0]=Pi/2. With this method you could also solve more difficult problems, like e.g. the pendulum equation: y''[tau]+T[tau]^2 Sin[y[tau]] == 0. Good luck Alois