Rubel's universal differential equation

Abstract

Fourth-order differential equations such as 16y′^my′² - 32y^myⁿy′ + 17y ⁰³ = 0 are developed. It is shown that the equation is “universal” in the sense that any continuous function can be approximated with arbitrary accuracy over the whole x axis by a solution y(x) of the equation. This solution is a piecewise polynomial of degree 9 and of class C ⁴.

• approximation theory
• polynomial splines