- #1
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- 553
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?