Re: How to NDSolve the differential equation
- To: mathgroup at smc.vnet.net
- Subject: [mg19625] Re: How to NDSolve the differential equation
- From: "Kevin J. McCann" <kevinmccann at Home.com>
- Date: Mon, 6 Sep 1999 04:20:41 -0400
- Organization: @Home Network
- References: <7qulo3$2r5@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Chee Lim, Look at your DE when x=0 with your IC. The whole thing is zero. When this happens NDSolve can't get any traction on the problem. Maybe you could try something like this instead: NDSolve[{x y''[x] + Sin[x] y'[x] + 2 x y[x] == 0, y[0.001] == 0, y'[0.001] == 1}, y, {x, 0.001, 2}] Alternatively, divide through by x and solve this DE: y''[x] + y'[x] Sin[x]/x + 2 y[x] == 0 again you will have problems at x=0, this time because of the Sin[x]/x; so, why not expand it: s[x_] = Normal[Series[Sin[x]/x, {x, 0, 12}]] This gives about 9-place accuracy over the [0,2] range. Then: q=y/.NDSolve[{y''[x] + y'[x] s[x]+ 2 y[x] == 0 , y[0] == 0, y'[0] == 1}, y, {x, 0, 2},WorkingPrecision->20][[1]] This gives a solution which satisfies the original DE to about 7 places. Plot[x q''[x] + q'[x]Sin[x] + 2x q[x], {x, 0, 2}, PlotRange -> {-0.000001, 0.000001}, PlotStyle -> RGBColor[1, 0, 0]]; Kevin Chee Lim Cheung <cheelc at mbox2.singnet.com.sg> wrote in message news:7qulo3$2r5 at smc.vnet.net... > Dear Mathematica gurus & users, > > I encountered error messages with the tag Power::infy when I tried to do > the following: > > NDSolve[{x y''[x] + Sin[x] y'[x] + 2 x y[x] == 0,y[0]==0, y'[0]==1}, y, > {x,0,2}] > > Can anyone help me in getting Mathematica to produce an answer? I am using > Mathematica 4.0 & Mathematica 3.0. > > Thanks > Chee >
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- Re: Re: How to NDSolve the differential equation
- From: "Carl K.Woll" <carlw@fermi.phys.washington.edu>
- Re: Re: How to NDSolve the differential equation