StepMonitor problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg127433] StepMonitor problem*From*: Daniel <dosadchy at its.jnj.com>*Date*: Wed, 25 Jul 2012 02:29:55 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

Hello, I use NDSolve to solve a differential system of equations and I need to plot the solution during the execution of NDSolve. I use the StepMonitor option. For a differential system it works great, at each step I get the time and the function values. But - for an algebraic-differential system it doesn't work. Instead of function values I get the function derivative values! (took me some time to realize that). The EvaluationMonitor correctly gives the function values. Do I use the StepMonitor correctly? Example to illustrate the problem: Solve an algebraic-differential system, while saving values with StepMonitor and EvaluationMonitor: {sol, {dataStep, dataEv}} = Reap[ NDSolve[{x'[t] == y[t]^2 + x[t] y[t], 2 x[t]^2 + y[t]^2 == 1, x[0] == 0}, {x, y}, {t, 0, 10}, StepMonitor :> Sow[{t, x[t], y[t]}, "stepMonitor"], EvaluationMonitor :> Sow[{t, x[t], y[t]}, "evaluationMonitor"] ], {"stepMonitor", "evaluationMonitor"}]; Plotting the solution and EvaluationMonitor shows correspondence: Plot[{x[t], y[t]} /. sol // Evaluate, {t, 0, 10}, PlotRange -> All] ListPlot[ Transpose[{dataEv[[1, All, 1]], #}] & /@ Transpose[dataEv[[1, All, 2 ;;]]], PlotRange -> All] Plotting the StepMonitor shows discrepancy: ListPlot[Transpose[{dataStep[[1, All, 1]], #}] & /@ Transpose[dataStep[[1, All, 2 ;;]]], PlotRange -> All] Plotting the solution derivatives shows correspondence to StepMonitor: Plot[{x'[t], y'[t]} /. sol // Evaluate, {t, 0, 10}, PlotRange -> All]