Leading-order term

There is no strict cut-off for when two terms should or should not be regarded as approximately the same order, or magnitude.

However, in between is a grey area, so there are no fixed boundaries where terms are to be regarded as approximately leading-order and where not.

Deciding whether terms in a model are leading-order (or approximately leading-order), and if not, whether they are small enough to be regarded as negligible, (two different questions), is often a matter of investigation and judgement, and will depend on the context.

[dubious – discuss] For example, the equation 100 = 1 + 1 + 1 + ... + 1, (where the right hand side comprises one hundred 1's).

These can be called the next-to-leading order (NLO) terms or corrections.

[3][16][17] For particular fluid flow scenarios, the (very general) Navier–Stokes equations may be considerably simplified by considering only the leading-order components.

Machine learning algorithms can partition simulation or observational data into localized partitions with leading-order equation terms for aerodynamics, ocean dynamics, tumor-induced angiogenesis, and synthetic data applications.

Graph of y = x 3 + 5 x + 0.1. The leading order, or main, behaviour at x = 0.001 is that y is constant, and at x = 10 is that y increases cubically with x .