Mahesh Yadav

Mahesh Yadav

COMPUTATIONAL STATISTICAL PHYSICS

Discrete error and convergence

less than 1 minute read

Published:

I was asked a question today about a typical way to present the error between a numerical scheme and an exact solution, and the convergence of the method. I will demonstrate one method that is typically used based on the $L_{2}$-norm of the norm.

Consider the ODE \(\frac{dx}{dt} = x(t) \qquad x(0) = 1\) which has the analytic solution

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