2 results about "Elliptic partial differential equation" patented technology

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 Auₓₓ+2Buₓy+Cuyy+Duₓ+Euy+Fu+G=0, where A, B, C, D, E, F, and G are functions of x and y and where uₓ=∂u/∂x and similarly for uₓₓ,uy,uyy,uₓy. A PDE written in this form is elliptic if B²-AC<0, with this naming convention inspired by the equation for a planar ellipse.