Question

A numerical method is total variation diminishing if __________

(a) the total variation remains constant with increasing time

(b) the total variation increases with increasing time

(c) the total variation does not increase with increasing time

(d) the total variation decreases with increasing time

This question was posed to me in a national level competition.

This intriguing question originated from High Resolution Schemes in chapter High Resolution Schemes of Computational Fluid Dynamics

Answer 1

The correct answer is (c) the total variation does not increase with increasing time

For explanation I would say: Any numerical method is said to be total variation diminishing if the total variation diminishes with time. This means that the value of total variation should not increase with time. It can either decrease or remain the same.