2 replaced http://mathematica.stackexchange.com/ with https://mathematica.stackexchange.com/ edited Apr 13 '17 at 12:55 NDSolve for EvaluationMonitor and StepMonitor. The Design of the NDSolve Framework for MethodMonitor. http://mathematica.stackexchange.com/questions/145/how-to-find-out-which-method-mathematica-selectedHow to find out which method Mathematica selected? for MethodMonitor http://mathematica.stackexchange.com/questions/102704/inspecting-step-size-and-order-of-tt-ndsolveinspecting step size and order of $\tt NDSolve$, a similar question with another answer that uses MethodMonitor. NDSolveSelf represents a method object, which takes arguments that are discussed in the tutorial NDSolve Method Plugin Framework. http://mathematica.stackexchange.com/questions/28337/whats-inside-interpolatingfunction1-4What's inside InterpolatingFunction[{{1., 4.}}, <>]? for getting the "Grid" from sol. Utility Packages for Numerical Differential Equation Solving for utilities such as StepDataPlot[] mentioned by @J.M. in a comment and getting the steps from the solution sol. NDSolve for EvaluationMonitor and StepMonitor. The Design of the NDSolve Framework for MethodMonitor. http://mathematica.stackexchange.com/questions/145/how-to-find-out-which-method-mathematica-selected for MethodMonitor http://mathematica.stackexchange.com/questions/102704/inspecting-step-size-and-order-of-tt-ndsolve, a similar question with another answer that uses MethodMonitor. NDSolveSelf represents a method object, which takes arguments that are discussed in the tutorial NDSolve Method Plugin Framework. http://mathematica.stackexchange.com/questions/28337/whats-inside-interpolatingfunction1-4 for getting the "Grid" from sol. Utility Packages for Numerical Differential Equation Solving for utilities such as StepDataPlot[] mentioned by @J.M. in a comment and getting the steps from the solution sol. NDSolve for EvaluationMonitor and StepMonitor. The Design of the NDSolve Framework for MethodMonitor. How to find out which method Mathematica selected? for MethodMonitor inspecting step size and order of $\tt NDSolve$, a similar question with another answer that uses MethodMonitor. NDSolveSelf represents a method object, which takes arguments that are discussed in the tutorial NDSolve Method Plugin Framework. What's inside InterpolatingFunction[{{1., 4.}}, <>]? for getting the "Grid" from sol. Utility Packages for Numerical Differential Equation Solving for utilities such as StepDataPlot[] mentioned by @J.M. in a comment and getting the steps from the solution sol. 1 answered Jan 28 '17 at 17:03 Michael E2 159k1313 gold badges217217 silver badges516516 bronze badges Ways to get information about an ODE solution sol = NDSolve[..., {x,..}, {t, a, b}]: Steps: x["Grid"] /. sol x["Coordinates"] /. sol Reap[NDSolve[..., StepMonitor :> Sow[t]] Method: Reap[NDSolve[..., MethodMonitor :> Sow[NDSolveSelf]] Trace[NDSolve[...], NDSolveInitializeMethod[__], TraceInternal -> True] Evaluations: Reap[NDSolve[..., EvaluationMonitor :> Sow[t]] Example (OP's but with a shorter interval of integration): Block[{nstep = 0, neval = 0}, {sol2, {steps2, methods2, eval2}} = Reap[NDSolve[{x1'[t] == x2[t], x2'[t] == -5 x2[t] - 44 y1[t] - 0.5 x1[t] y1[t] + Sin[5 t], y1'[t] == y2[t], y2'[t] == -3 y2[t] - 2 x2[t] + x1[t] y1[t]^2 + Cos[5 t], x1[0] == 0.1, x2[0] == 0.02, y1[0] == 0.2, y2[0] == 0.01}, {x1, x2, y1, y2}, {t, 0.1}, Method -> Fehlberg45, StepMonitor :> (Sow[{++nstep, t}, "Step"];), "MethodMonitor" :> (Sow[NDSolveSelf, "Method"];), EvaluationMonitor :> (Sow[{++neval, nstep, t}, "Evaluation"];), MaxStepFraction -> 1], (* allow longer steps because of short interval *) {"Step", "Method", "Evaluation"}] ];  A presentations of the steps & evaluation times: Grid[ Join[ {{"Step", "Evaluations", SpanFromLeft}}, MapIndexed[Join[#2, #1] &, SplitBy[First@eval2, #[[2]] &][[All, All, 3]]] ], Alignment -> {Left, Automatic}]  methods2[[1, 1]] // Short  x1["Grid"] /. sol2 (*{{{0.},{0.0115275},{0.0280347},{0.0448688},{0.0620601},{0.0795363}, {0.0897682},{0.1}}}*)  Note that the default method "LSODA" does not use "MethodMonitor". Use Trace[] to see the NDSolveLSODA method object it uses. References: NDSolve for EvaluationMonitor and StepMonitor. The Design of the NDSolve Framework for MethodMonitor. http://mathematica.stackexchange.com/questions/145/how-to-find-out-which-method-mathematica-selected for MethodMonitor http://mathematica.stackexchange.com/questions/102704/inspecting-step-size-and-order-of-tt-ndsolve, a similar question with another answer that uses MethodMonitor. NDSolveSelf represents a method object, which takes arguments that are discussed in the tutorial NDSolve Method Plugin Framework. http://mathematica.stackexchange.com/questions/28337/whats-inside-interpolatingfunction1-4 for getting the "Grid" from sol. Utility Packages for Numerical Differential Equation Solving for utilities such as StepDataPlot[] mentioned by @J.M. in a comment and getting the steps from the solution sol.