Re: NDSolve for catenary
- To: mathgroup at smc.vnet.net
- Subject: [mg111378] Re: NDSolve for catenary
- From: "Kevin J. McCann" <Kevin.McCann at umbc.edu>
- Date: Thu, 29 Jul 2010 06:44:57 -0400 (EDT)
- References: <i2ok69$7sd$1@smc.vnet.net>
Your problem is likely in the attempt to solve a boundary value problem
rather than an initial value problem. Here is a quick shooting method
that gets the answer:
(* Define the shooter. Takes an initial slope of a and returns r[1] *)
Clear[shoot, a]
shoot[a_?NumberQ] := Module[{r, x, y},
y = r /. NDSolve[{1 +
\!\(\*SuperscriptBox["r", "\[Prime]",
MultilineFunction->None]\)[x]^2 - r[x]
\!\(\*SuperscriptBox["r", "\[Prime]\[Prime]",
MultilineFunction->None]\)[x] == 0, r[0] == 1, r'[0] == a},
r, {x, 0, 1}][[1]];
y[1]
]
(* Find the correct initial slope *)
\[Alpha] = a /. FindRoot[shoot[a] == 1, {a, -1, 1}]
(* Now that we have the correct slope, solve the DE *)
R = r /. NDSolve[{1 +
\!\(\*SuperscriptBox["r", "\[Prime]",
MultilineFunction->None]\)[x]^2 - r[x]
\!\(\*SuperscriptBox["r", "\[Prime]\[Prime]",
MultilineFunction->None]\)[x] == 0, r[0] == 1, r'[0] == \[Alpha]},
r, {x, 0, 1}][[1]]
(* Plot it *)
Plot[R[x], {x, 0, 1}, PlotRange -> {0.5, 1}]
Kevin
Sam Takoy wrote:
> Hi,
>
> This:
>
> NDSolve[{ 1 + r'[x]^2 - r[x] r''[x] == 0, r[0] == r[1] == 1}, r, {x, 0, 1}]
>
> should solve the catenary problem, but it gives 1/0 errors. Can you
> suggest a fix?
>
> Many thanks!
>
> Sam
>