Re: NDSolve::ndsz question
- To: mathgroup at smc.vnet.net
- Subject: [mg63676] Re: NDSolve::ndsz question
- From: BGHEkaya at gmail.com
- Date: Mon, 9 Jan 2006 04:49:37 -0500 (EST)
- References: <dpnqoa$6rh$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Flip, The easiest way to extend the integration using NDSolve is to work with exact arithmetic. Thus you can readily solve for x=400 with high accuracy κ = 400000000; β = 23/10000; ϵ = 24/1000; sol = NDSolve[{y'[x] == -κ x^(-1/2)\[ExponentialE]^(-ϵ x)( y[x]^2 - (β x^2BesselK[2, x])^2), y[1/10] == β BesselK[2, 1/10]/(1/10)}, y, {x, 1/10, 2000}, WorkingPrecision -> 30, MaxSteps -> Infinity] For large x the solution to the ODE is y[x]~-(Sqrt[ϵ]/(Sqrt[ϵ]*C[1] + Sqrt[Pi]*κ* Erf[Sqrt[x]*Sqrt[ϵ]])) and thus as x->Infinity, y[x] tends to a constant value given by -(Sqrt[ϵ]/(Sqrt[ϵ]*C[1] + Sqrt[Pi]*κ)) We can use the numerical value of y[400] to evaluate the constant of integration C[1] I found this value to be 5.824503762*^-10 By increasing the accuracy of NDSolve you can improve on this value. Hope this helps, Cheers, Brian