parabolic differential equation

parabolic differential equation

[¦par·ə¦bäl·ik ‚dif·ə′ren·chəl i′kwā·zhən]
(mathematics)
A general type of second-order partial differential equation which includes the heat equation and has the form where the Ai j , Bi , C, and F are suitably differentiable real functions of x1, x2, …, xn , and there exists at each point (x1, …, xn ) a real linear transformation on the xi which reduces the quadratic form to a sum of fewer than n squares, not necessarily all of the same sign, while the same transformation does not reduce the Bi to 0. Also known as parabolic partial differential equation.
References in periodicals archive ?
Simultaneous space-time adaptive wavelet solution of nonlinear parabolic differential equations.
The judges summarised the winning paper as "an excellent technical work proposing a new numerical method for the efficient solution of parabolic differential equations.