TommySnowman

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10 years, 163 days

MaplePrimes Activity


These are replies submitted by TommySnowman

Hi, thanks for your help.

 

I agree that the issue is probably my use of the expand function, although I disagree

that the TotEr should be infinite. I think Maple is making an error here - I mean look

at the following:

> int(subs([k[0] = 3, k[1] = .2, k[2] = .1, x[1](0) = 0, x[2](0) = 30], ErTime),
 t = 0 .. 100);
4.999546030
> int(subs([k[0] = 3, k[1] = .2, k[2] = .1, x[1](0) = 0, x[2](0) = 30], ErTime), 
t = 0 .. 1000);
5.000000098
> int(subs([k[0] = 3, k[1] = .2, k[2] = .1, x[1](0) = 0, x[2](0) = 30], ErTime), 
t = 0 .. 10000);
5.000000998
> int(subs([k[0] = 3, k[1] = .2, k[2] = .1, x[1](0) = 0, x[2](0) = 30], ErTime), 
t = 0 .. 100000);
5.000009998
> int(subs([k[0] = 3, k[1] = .2, k[2] = .1, x[1](0) = 0, x[2](0) = 30], ErTime), 
t = 0 .. 10000000);
5.000999998
> int(subs([k[0] = 3, k[1] = .2, k[2] = .1, x[1](0) = 0, x[2](0) = 30], ErTime), 
t = 0 .. 1000000000);
5.099999998
> int(subs([k[0] = 3, k[1] = .2, k[2] = .1, x[1](0) = 0, x[2](0) = 30], ErTime), 
t = 0 .. 100000000000);
15.00000000
 
This seems very odd to me, and I can see no way in which the function would jump 
back into 'life' like this. 

Hi, thanks for your help.

 

I agree that the issue is probably my use of the expand function, although I disagree

that the TotEr should be infinite. I think Maple is making an error here - I mean look

at the following:

> int(subs([k[0] = 3, k[1] = .2, k[2] = .1, x[1](0) = 0, x[2](0) = 30], ErTime),
 t = 0 .. 100);
4.999546030
> int(subs([k[0] = 3, k[1] = .2, k[2] = .1, x[1](0) = 0, x[2](0) = 30], ErTime), 
t = 0 .. 1000);
5.000000098
> int(subs([k[0] = 3, k[1] = .2, k[2] = .1, x[1](0) = 0, x[2](0) = 30], ErTime), 
t = 0 .. 10000);
5.000000998
> int(subs([k[0] = 3, k[1] = .2, k[2] = .1, x[1](0) = 0, x[2](0) = 30], ErTime), 
t = 0 .. 100000);
5.000009998
> int(subs([k[0] = 3, k[1] = .2, k[2] = .1, x[1](0) = 0, x[2](0) = 30], ErTime), 
t = 0 .. 10000000);
5.000999998
> int(subs([k[0] = 3, k[1] = .2, k[2] = .1, x[1](0) = 0, x[2](0) = 30], ErTime), 
t = 0 .. 1000000000);
5.099999998
> int(subs([k[0] = 3, k[1] = .2, k[2] = .1, x[1](0) = 0, x[2](0) = 30], ErTime), 
t = 0 .. 100000000000);
15.00000000
 
This seems very odd to me, and I can see no way in which the function would jump 
back into 'life' like this. 

Thank you for your help.

I don't expect the integral to be zero. Any confusion is probably due to my lack of clarity though, apologies about that.

Rather, the spurious result that maple gives me (almost certainly due to my own spurious use of the expand function) suggests that the integral, even with the absolute values, gives zero error in the specific case where k_0 = k_2 x_{2}(0). The plots I showed demonstrate that this can't be true.

As for why I am interested in having the absolute value of the error - I only want zero error in the case where the two curves are identical. Not where the area before and after crossing cancel out. I want this to be the case because otherwise my approximation would appear to be a good predictor of the exact result for all times when it is not.

Thank you for your help.

I don't expect the integral to be zero. Any confusion is probably due to my lack of clarity though, apologies about that.

Rather, the spurious result that maple gives me (almost certainly due to my own spurious use of the expand function) suggests that the integral, even with the absolute values, gives zero error in the specific case where k_0 = k_2 x_{2}(0). The plots I showed demonstrate that this can't be true.

As for why I am interested in having the absolute value of the error - I only want zero error in the case where the two curves are identical. Not where the area before and after crossing cancel out. I want this to be the case because otherwise my approximation would appear to be a good predictor of the exact result for all times when it is not.

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