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# "AccuracyGoal" and NDSolve

Posted 10 years ago
 Hi! I would like to know how "AccuracyGoal" works. I know that "AccuracyGoal" is an option for various numerical operations which specifies how many effective digits of accuracy should be sought in the final result" so i tought that if I choose a bigger value the results should be more accurate, but if I put, for example AccuracyGoal->2 I obtain results that are completly different from the results I obtein with AccuracyGoal->4... It seems that a bigger value brings to a worse result and if I reach AccuracyGoal->10 the results disappear! I also have another point: I plot the evolution of a function (displacement) in the time. I plot the displacement of a point in the x direction and y direction. In both the directions the situation is the same but the solicitation in direction y is 30% of that in x. So I expect that the displacements follow the same evolution but one is simply smaller than the other. This is true and I can see it in the output but just until a certain time (about 20 seconds, while the time history lasts more than 40 seconds). So, I don't understand...what happen from second 20?! 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-0.0104, -0.0101, 0.0015, 0.008, 0.0071, 0.0027, -0.0002, 0.0004, 0.002, 0.0023, 0.0017, 0.0012, 0.001, 0.001, 0.001, 0.0009, 0.0009, 0.0009, 0.0008, 0.0008, 0.0008, 0.0008, 0.0008, 0.0007, 0.0007, 0.0007, 0.0007, 0.0007, 0.0007, 0.0007, 0.0007, 0.0007, 0.0007, 0}; ListLinePlot[mList, PlotRange -> {{0, Length[mList]}, {Min[mList], Max[mList]}}] ListLinePlot[(0.3*mList), PlotRange -> {{0, Length[mList]}, {0.3*Min[mList], 0.3*Max[mList]}}] GetIndex[t_] := IntegerPart[t/dT] + 1; mList[[GetIndex[0.04]]] GetGroundAcceleration[t_] := mList[[GetIndex[ t]]] + (mList[[GetIndex[t] + 1]] - mList[[GetIndex[t]]]) FractionalPart[ t/dT]; GetGroundAcceleration[40] ( Force-Displacement) \[Mu] = 0.033; g = 9.81; R = 3.7; \[Omega] = Sqrt[g/R]; YP = 0.001; W = 726992.03; \[Gamma] = 0.5; tTotal = 45; n = 5; ParametricPlot[ Evaluate[{x1[t], (1/R)*x1[t] + \[Mu]*x3[t]} /. Quiet@NDSolve[ {x1'[t] == x5[t], x2'[t] == x6[t], x3'[t] == x5[t]/YP (1 - Abs[x3[t]]^n* (\[Gamma] *Sign[x5[t]* x3[t]] + (1 - \[Gamma]))), x4'[t] == x6[t]/YP (1 - Abs[x3[t]]^n* (\[Gamma] *Sign[x6[t]* x4[t]] + (1 - \[Gamma]))), x5'[t] == -(\[Omega]^2)*x1[t] - \[Mu]*9.81*x3[t] - 9.81*GetGroundAcceleration[t], x6'[t] == -(\[Omega]^2)*x2[t] - \[Mu]*9.81*x4[t] - 9.81*0.3*GetGroundAcceleration[t], x1[0] == 0, x2[0] == 0, x3[0] == 0, x4[0] == 0, x5[0] == 0, x6[0] == 0}, {x1[t], x2[t], x3[t], x4[t], x5[t], x6[t]}, {t, 0, tTotal}, AccuracyGoal -> 2]], {t, 0, tTotal}, ImageSize -> {500, 500}, PlotRange -> {{-0.5, 0.5}, {-0.2, 0.2}}, AspectRatio -> 1/1, AxesLabel -> {"ux", "F"}] ParametricPlot[ Evaluate[{x2[t], (1/R)*x2[t] + \[Mu]*x4[t]} /. Quiet@NDSolve[ {x1'[t] == x5[t], x2'[t] == x6[t], x3'[t] == x5[t]/YP (1 - Abs[x3[t]]^n* (\[Gamma] *Sign[x5[t]* x3[t]] + (1 - \[Gamma]))), x4'[t] == x6[t]/YP (1 - Abs[x3[t]]^n* (\[Gamma] *Sign[x6[t]* x4[t]] + (1 - \[Gamma]))), x5'[t] == -(\[Omega]^2)*x1[t] - \[Mu]*9.81*x3[t] - 9.81*GetGroundAcceleration[t], x6'[t] == -(\[Omega]^2)*x2[t] - \[Mu]*9.81*x4[t] - 9.81*0.3*GetGroundAcceleration[t], x1[0] == 0, x2[0] == 0, x3[0] == 0, x4[0] == 0, x5[0] == 0, x6[0] == 0}, {x1[t], x2[t], x3[t], x4[t], x5[t], x6[t]}, {t, 0, tTotal}, AccuracyGoal -> 5]], {t, 0, tTotal}, ImageSize -> {500, 500}, PlotRange -> {{-0.1, 0.1}, {-0.05, 0.05}}, AspectRatio -> 1/1, AxesLabel -> {"uy", "F"}] (* Displacement (time)*) ParametricPlot[ Evaluate[{t, x1[t]} /. Quiet@NDSolve[ {x1'[t] == x5[t], x2'[t] == x6[t], x3'[t] == x5[t]/YP (1 - Abs[x3[t]]^n* (\[Gamma] *Sign[x5[t]* x3[t]] + (1 - \[Gamma]))), x4'[t] == x6[t]/YP (1 - Abs[x3[t]]^n* (\[Gamma] *Sign[x6[t]* x4[t]] + (1 - \[Gamma]))), x5'[t] == -(\[Omega]^2)*x1[t] - \[Mu]*9.81*x3[t] - 9.81*GetGroundAcceleration[t], x6'[t] == -(\[Omega]^2)*x2[t] - \[Mu]*9.81*x4[t] - 9.81*0.3*GetGroundAcceleration[t], x1[0] == 0, x2[0] == 0, x3[0] == 0, x4[0] == 0, x5[0] == 0, x6[0] == 0}, {x1[t], x2[t], x3[t], x4[t], x5[t], x6[t]}, {t, 0, tTotal}, AccuracyGoal -> 2]], {t, 0, tTotal}, ImageSize -> {500, 500}, PlotRange -> {{0, tTotal}, {-0.4, 0.4}}, AspectRatio -> 1/1, AxesLabel -> {"t", "ux"}] ParametricPlot[ Evaluate[{t, x2[t]} /. Quiet@NDSolve[ {x1'[t] == x5[t], x2'[t] == x6[t], x3'[t] == x5[t]/YP (1 - Abs[x3[t]]^n* (\[Gamma] *Sign[x5[t]* x3[t]] + (1 - \[Gamma]))), x4'[t] == x6[t]/YP (1 - Abs[x3[t]]^n* (\[Gamma] *Sign[x6[t]* x4[t]] + (1 - \[Gamma]))), x5'[t] == -(\[Omega]^2)*x1[t] - \[Mu]*9.81*x3[t] - 9.81*GetGroundAcceleration[t], x6'[t] == -(\[Omega]^2)*x2[t] - \[Mu]*9.81*x4[t] - 9.81*0.3*GetGroundAcceleration[t], x1[0] == 0, x2[0] == 0, x3[0] == 0, x4[0] == 0, x5[0] == 0, x6[0] == 0}, {x1[t], x2[t], x3[t], x4[t], x5[t], x6[t]}, {t, 0, tTotal}, AccuracyGoal -> 2]], {t, 0, tTotal}, ImageSize -> {500, 500}, PlotRange -> {{0, tTotal}, {-0.3, 0.3}}, AspectRatio -> 1/1, AxesLabel -> {"t", "uy"}] Thanks!