Heun

Heun is a German surname. The most notable bearer is Karl Heun, a German mathematician who worked in the late 19th and early 20th centuries. Several mathematical concepts are named after him, reflecting his contributions to the theory of differential equations.

In mathematics, the name Heun appears in two principal objects. Heun's method is a numerical technique for solving ordinary differential equations. It is a simple explicit Runge–Kutta method of order two, often described as an improved Euler method. The procedure estimates the next value by computing two slope estimates—one at the beginning of the interval and one at the end—and averaging them to advance the solution. This provides greater accuracy than the basic Euler method while remaining computationally straightforward.

The Heun equation is a second-order linear differential equation with four regular singular points, typically at z = 0, z = 1, z = a, and infinity. It generalizes the hypergeometric equation, and its solutions are known as Heun functions. The Heun equation arises in various areas of mathematical physics, including problems in quantum mechanics and general relativity, under suitable parameter choices or coordinate transformations.

Beyond these, Heun as a surname appears in other historical mathematical literature. The term “Heun” thus commonly signals either the mathematician Karl Heun or the numerical and analytic concepts named in his honor.