Why can”t I get a smooth curve?

Question

I used "Table" to calculate and plot the following complicated function. First, we choose an initial value for $G$ and other parameters, but at later times $G$ changes with function $I_a$.

Y = 1; r1 = .3; r2 = .3; G = 0.35;
points = Table[L = G - Y; w = Sqrt[-4 + G^2 + 2 G Y + Y^2];

Ia = 1/(
   8 w^2) (Cosh[2 L t] + Sinh[2 L t]) (8 + 2 G^2 - 2 w^2 + 
     4 G Y + 2 Y^2 - 2 (G^2 - w^2 + 2 G Y + Y^2) Cosh[2 r1] - 
     8 Cosh[2 r2] - 8 Cosh[2 t w] - 2 G^2 Cosh[2 t w] - 
     2 w^2 Cosh[2 t w] - 4 G Y Cosh[2 t w] - 2 Y^2 Cosh[2 t w] + 
     G^2 Cosh[2 (r1 - t w)] + w^2 Cosh[2 (r1 - t w)] + 
     2 G Y Cosh[2 (r1 - t w)] + Y^2 Cosh[2 (r1 - t w)] + 
     4 Cosh[2 (r2 - t w)] + G^2 Cosh[2 (r1 + t w)] + 
     w^2 Cosh[2 (r1 + t w)] + 2 G Y Cosh[2 (r1 + t w)] + 
     Y^2 Cosh[2 (r1 + t w)] + 4 Cosh[2 (r2 + t w)] - 
     4 G w Sinh[2 t w] - 4 w Y Sinh[2 t w] - 
     2 G w Sinh[2 (r1 - t w)] - 2 w Y Sinh[2 (r1 - t w)] + 
     2 G w Sinh[2 (r1 + t w)] + 2 w Y Sinh[2 (r1 + t w)]) + 
  Integrate[(
   E^(2 L (t - u) - 
     2 (t + u) w) (E^(2 u w) (-G + w - Y) + 
      E^(2 t w) (G + w + Y))^2)/(4 w^2), {u, 0, t}] // Chop;


 G = 1/(1 + Ia/.05);

 {{t, Ia}, {t, G}}, {t, 0, 10, .05}];
Iapoints = Map[First, points];
varpoints = Map[Last, points];


ListLinePlot [Iapoints,PlotRange -> All]

ListLinePlot [varpoints,PlotRange -> All]

The output seems good to this point. But if I change the initial values as

Y = 2.2; r1 = .3; r2 = .3; G = 1.96;

and

G = 2/(1 + Ia/5)

then the output does not seem good. I couldn't upload the figure because I don't know how imgur works!

Anyway, I think the irregularities in the plots are due to error accumulation. I want to try a for loop that does the same job and see if the errors are still there or I can get a good plot for any parameters. But I don't know how to write a "for loop" for this problem.

Answer 1

here is your "for loop" with the same "ill-conditioned plot"

An explanation for the "strange" plot:
If you use ListPlot instead of ListLinePlot you will see that the points which formed a straight line in your first example, in the second, they are grouped in 2 groups half moving up and half moving down (alternating) as the denominator of Ia changes from 5 to .05

Y = 2.2; r1 = .3; r2 = .3; G = 1.96;
points = {};
For[t = 0, t <= 10, t = t + .05, L = G - Y; 
w = Sqrt[-4 + G^2 + 2 G Y + Y^2];
Ia = 1/(8 w^2) (Cosh[2 L t] + Sinh[2 L t]) (8 + 2 G^2 - 2 w^2 + 
    4 G Y + 2 Y^2 - 2 (G^2 - w^2 + 2 G Y + Y^2) Cosh[2 r1] - 
    8 Cosh[2 r2] - 8 Cosh[2 t w] - 2 G^2 Cosh[2 t w] - 
    2 w^2 Cosh[2 t w] - 4 G Y Cosh[2 t w] - 2 Y^2 Cosh[2 t w] + 
    G^2 Cosh[2 (r1 - t w)] + w^2 Cosh[2 (r1 - t w)] + 
    2 G Y Cosh[2 (r1 - t w)] + Y^2 Cosh[2 (r1 - t w)] + 
    4 Cosh[2 (r2 - t w)] + G^2 Cosh[2 (r1 + t w)] + 
    w^2 Cosh[2 (r1 + t w)] + 2 G Y Cosh[2 (r1 + t w)] + 
    Y^2 Cosh[2 (r1 + t w)] + 4 Cosh[2 (r2 + t w)] - 
    4 G w Sinh[2 t w] - 4 w Y Sinh[2 t w] - 
    2 G w Sinh[2 (r1 - t w)] - 2 w Y Sinh[2 (r1 - t w)] + 
    2 G w Sinh[2 (r1 + t w)] + 2 w Y Sinh[2 (r1 + t w)]) + 
 Integrate[(E^(2 L (t - u) - 
        2 (t + u) w) (E^(2 u w) (-G + w - Y) + 
        E^(2 t w) (G + w + Y))^2)/(4 w^2), {u, 0, t}] // Chop;
 G = 2/(1 + Ia/5);
AppendTo[points, {{t, Ia}, {t, G}}]];
Iapoints = Map[First, points];
varpoints = Map[Last, points];

ListLinePlot[Iapoints, PlotRange -> All]

ListLinePlot[varpoints, PlotRange -> All]