Elliptic partial differential equation
Class of second-order linear partial differential equations / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Elliptic partial differential equation?
Summarize this article for a 10 year old
Second-order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic. Any second-order linear PDE in two variables can be written in the form
where A, B, C, D, E, F, and G are functions of x and y and where , and similarly for . A PDE written in this form is elliptic if
with this naming convention inspired by the equation for a planar ellipse. Equations with are termed parabolic while those with are hyperbolic.
The simplest examples of elliptic PDE's are the Laplace equation, , and the Poisson equation, In a sense, any other elliptic PDE in two variables can be considered to be a generalization of one of these equations, as it can always be put into the canonical form