Re: Checking the Results of NDSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg37268] Re: Checking the Results of NDSolve*From*: Tom Burton <tburton at brahea.com>*Date*: Mon, 21 Oct 2002 02:29:36 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

On 10/18/02 2:26 AM, in article aook3e$pij$1 at smc.vnet.net, "Thomas Steger" <steger at uni-greifswald.de> wrote: > I use NDSolve to approximate a 6-dimensional and highly non-linear > dynamic system numerically. > > QUESTION: What are usual (and simple) techniques to check the > reliability of the resulting numerical solution? I would check the the boundary conditions and then plot the residual error from the differential equation. Here is an example with all output deleted. possibilities = NDSolve[{y[x]^4 + y'[x]^3 == 0, y[0] - 1 == 0}, y[x], {x, 0, 1}] yy[x_] = y[x] /. possibilities SHOW RESULTS Needs["Graphics`Colors`"]; SetOptions[Plot, PlotStyle -> ({Thickness[0.01], #1} & ) /@ {Red,Green,Blue} ]; Plot[Evaluate[Re[yy[x]]], {x, 0, 1}] Plot[Evaluate[Im[yy[x]]], {x, 0, 1}] CHECK INITIAL CONDITIONS yy[0] - 1 PREPARE AND SHOW RESIDUAL res[x_] = yy[x]^4 + yy'[x]^3 Plot[Evaluate[Re[res[x]]], {x, 0, 1}] Plot[Evaluate[Im[res[x]]], {x, 0, 1}] Plot[Evaluate[Re[res[x]]], {x, 0, 0.001}, PlotRange -> All] Plot[Evaluate[Im[res[x]]], {x, 0, 0.001}, PlotRange -> All]