Re: Can Mathematica solve this differential equation ?
- To: mathgroup at smc.vnet.net
- Subject: [mg107109] Re: Can Mathematica solve this differential equation ?
- From: "Nasser M. Abbasi" <nma at 12000.org>
- Date: Wed, 3 Feb 2010 06:08:43 -0500 (EST)
- References: <hk8nlh$8h4$1@smc.vnet.net>
"Ashok" <nils_von_nostrand at yahoo.com> wrote in message news:hk8nlh$8h4$1 at smc.vnet.net... > In beam bending, we have the following situation: > > y '' [x] = M(x), boundary conditions specified for y[0] and y[1] > > Simple enough, but the problem arises as M is a piecewise-defined > function (linear in all pieces though) > > i.e., M(x) = M1(x) for 0<x<1 > and M(x) = M2(x) for 1<x<2 > M(x) = 0 for all other values of x > > Obviously, we are only interested in the interval 0<x<1 > > This leads to two separate equations: > > y1'' [x] = M1(x) in 0<x<1 > y2 '' [x] = M2(x) in 1 <x <2 > > Now we will have 4 constants of integration. We therefore need 4 > equations to solve for them. Two of them are obtained from the > specified boundary conditions for y[0] and y[1]. The other two come > from continuity equations: > y1[1] = y2[1] and y1 ' [1] = y2 ' [1]. It is these last two that > totally throw me off. I do not understand how to put them into > Mathematica. > > Any help is appreciated. > > Thank you > > Ashok > One way to solve the first ode and use its results as initial conditions for the second ode? Here is an example: Clear[x,M1,M2,y1,y2] M1=x; M2=2 x; First@DSolve[{y1''[x]==M1,y1[0]==0,y1[1]==1},y1[x],x]; y1=y1[x]/.% Out[44]= 1/6 (5 x+x^3) First@DSolve[{y2''[x]==M2,y2[1]==y1/.x->1,y2'[1]==D[y1,x]/.x->1},y2[x],x]; y2=y2[x]/.% Out[47]= 1/3 (1+x+x^3) --Nasser