I'd just like to know if it is possible to evaluate the error of a numerical scheme by using it's solutions integral?
To elaborate this. I have long transmission line, which I evaluate over time numerically. I also have the exact solution on any point at any time. What I'd like to do is to plot the function of the starting (or end) point over time, as well as it's numerically simulated value over time. Approximating their integrals in MATLAB and subtracting them.
Is this value a valid measurement for the error or - when using multiple numerical schemes - a suitable validation which one is better for this case?
Kind regards
The integral of the raw error (or the average error) can be a poor measure, because if the error alternates in sign, the positive and negative contributions will cancel out.
Prefer the integral of the absolute error or the squared error.
Another measure can be useful (but does not involve an integral): the maximum absolute error.