numerical instability

[Willi Braun]

Following model behaves numerical instable:

loadString("
model testCFExpr1
  Real x;
initial equation
  der(x) = 3.14159/2;
equation
  sin(der(x)) = cos(x);
end testCFExpr1;
");

simulate(testCFExpr1, stopTime=10, tolerance=1e-4);
val(x,0);
val(x,10);

val(der(x),0);
val(der(x),10);

simulate(testCFExpr1, stopTime=10, tolerance=1e-5);
val(x,0);
val(x,10);

val(der(x),0);
val(der(x),10);

simulate(testCFExpr1, stopTime=10, tolerance=1e-6);
val(x,0);
val(x,10);

val(der(x),0);
val(der(x),10);

simulate(testCFExpr1, stopTime=10, tolerance=1e-7);
val(x,0);
val(x,10);

val(der(x),0);
val(der(x),10);

simulate(testCFExpr1, stopTime=10, tolerance=1e-8);
val(x,0);
val(x,10);

val(der(x),0);
val(der(x),10);

results with different tolerances:

tolerance = 0.0001:
-0.000001326803844565571
1.5707084777514067
1.570795
0.00008784904348996832

tolerance = 0.00001:
-0.000001326803844565571
1.5707236871192907
1.570795
0.00007263967560595125

tolerance = 0.000001:
-0.000001326803844565571
526.3524099363941
1.570795
18.985196381642503

tolerance = 0.0000001:
-0.000001326803844565571
1.570724934665874
1.570795
0.00007139212902257958

tolerance = 0.00000001:
-0.000001326803844565571
183.5349266542149
1.570795
0.24824358078800488