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From: Gediz GÜRSU on 16 Feb 2010 10:29
Good Day Everyone;
1) What is the theoretical low limit of error in MATLAB ?

I am trying to increase solution accuracy of an ode related forced vibration 'D2x+x=cos(2*pi*t)'

As you see its simple, lineer mass and spring system forced at 1 Hz Freq.
The Approach I use I am solving this system using
ode113 with options RelTol=realmin AbsTol=realmin for IC [0 0] and tspan [0 10] (num)
symbolic solver dsolve same IC and same tspan (analytic)

Then I interpolate results to a T_INTP=0:0.01:10 vector;
and plot absolute error err=abs(Xnum-Xan)./Xan;

However I cant get lower error than 1e-11; And error increases at stationary points close to zero dramatically.

Is this error checking correct ?
Can we change machine epsylon ?
Is getting an error around 1e-64 possible and how ?

Please advise ...
Thank You

Gediz GURSU

PS: I read all help files. After Grasping the error and tolerances issue I ll planning to MDOF Nonlinear system to simulate energy transition. So I need to understand this part firmly.
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