ParametricNDSolve for a contact problem

• To: mathgroup at smc.vnet.net
• Subject: [mg131832] ParametricNDSolve for a contact problem
• From: Simon Pearce <Simon.Pearce at nottingham.ac.uk>
• Date: Sat, 12 Oct 2013 02:38:26 -0400 (EDT)
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• References: <20131010205057.5B2C26A2D@smc.vnet.net>

```Hi Mathgroup,

I've just installed v9.0.1.0, and I was hopeful that ParametricNDSolve would help simplify my code for solving a contact problem. I have an ODE which I don't know the starting point at which my initial conditions are to be set, which I need to vary.

The following toy model works, and shows that the range of integration may be set as a parameter:

sol1 = ParametricNDSolve[{y'[t] == y[t], y[0] == 0}, y, {t, b, 1}, {b}];
y[0] /. sol1

Whereas when the initial condition is to be set at the parameterised starting point it does not work:

sol2 = ParametricNDSolve[{y'[t] == y[t], y[b] == 0}, y, {t, b, 1}, {b}];
y[0] /. sol2

Any idea on how to get ParametricNDSolve to do this for me? My current method is to use NDSolve`ProcessEquations and NDSolve`Reinitialize inside a function which I send to FindRoot.

My actual problem is a highly nonlinear fifth order system, with one of the initial conditions at the unknown contact point also unknown.

Thanks,
Simon Pearce
University of Nottingham, UK
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