# Solving ODEs with large parameters in Mathematica 9

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1. Jul 24, 2014

### WannabeNewton

I have an ODE $e^{2x}H(Hv'(x) + H'v' + Hv'') + (k^2 - 2e^{2x}H^2(1 + \frac{H'}{2H}))v = 0$ where $H(x)$ is a known function that Mathematica has stored as an interpolation from a previous ODE and $v(x)$ is the unknown function to be solved for. $k$ is the adjustable parameter. Using ParametricNDSolve, Mathematica has no problem solving for an interpolation of $v$ if $k$ is very small e.g. on the order of $10^{-3}$ or even on the order of unity. But I have to solve for $v$ using values of $k$ that are of the order $10^7$ to $10^{12}$. Right now I'm running ParametricNDSolve for $k \sim 10^7$ and it is taking ages to solve for $v$. In fact I don't know if it actually will eventually solve for $v$ in a reasonable amount of time. If it doesn't solve it in a reasonable amount of time then I have no hope of ParametricNDSolve solving it in uniform steps between $k \sim 10^7$ and $k \sim 10^{12}$. Is there a reasonable way to work around this?

2. Aug 10, 2014