# Linearized differential equation

From AMS Glossary

## linearized differential equation

A differential equation that has been derived from an original nonlinear equation by the treatment of each dependent variable as consisting of the sum of an undisturbed or steady component and a small perturbation or deviation from this mean.

It is assumed that the product of two perturbation quantities is negligible compared to the first-order terms in the perturbations or to the undisturbed variables. This process of linearization, often called the method of small perturbations, leads to a linear differential equation with the perturbations of the original dependent variables as the new dependent variables. It has been used successfully to solve problems involving sound waves, gravity waves, frontal waves, tides, waves in the upper westerlies, and flow over hills and mountains.

Haurwitz, B. 1951. Compendium of Meteorology. 401–420.

Panofsky, H. 1954. Introduction to Dynamic Meteorology. ch. 4.