nonlinear parabolic equation

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• Parabolic partial differential equation — A parabolic partial differential equation is a type of second order partial differential equation, describing a wide family of problems in science including heat diffusion and stock option pricing. These problems, also known as evolution problems …   Wikipedia

• Nonlinear conjugate gradient method — In numerical optimization, the nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization. For a quadratic function : The minimum of f is obtained when the gradient is 0: . Whereas linear conjugate… …   Wikipedia

• Partial differential equation — A visualisation of a solution to the heat equation on a two dimensional plane In mathematics, partial differential equations (PDE) are a type of differential equation, i.e., a relation involving an unknown function (or functions) of several… …   Wikipedia

• Differential equation — Not to be confused with Difference equation. Visualization of heat transfer in a pump casing, created by solving the heat equation. Heat is being generated internally in the casing and being cooled at the boundary, providing a steady state… …   Wikipedia

• Heat equation — The heat equation is an important partial differential equation which describes the distribution of heat (or variation in temperature) in a given region over time. For a function of three spatial variables ( x , y , z ) and one time variable t ,… …   Wikipedia

• List of nonlinear partial differential equations — In mathematics and physics, nonlinear partial differential equations are (as their name suggests) partial differential equations with nonlinear terms. They describe many different physical systems, ranging from gravitation to fluid dynamics, and… …   Wikipedia

• Hamilton–Jacobi equation — In physics, the Hamilton–Jacobi equation (HJE) is a reformulation of classical mechanics and, thus, equivalent to other formulations such as Newton s laws of motion, Lagrangian mechanics and Hamiltonian mechanics. The Hamilton–Jacobi equation is… …   Wikipedia

• Convection–diffusion equation — The convection–diffusion equation is a parabolic partial differential equation combining the diffusion equation and the advection equation, which describes physical phenomena where particles or energy (or other physical quantities) are… …   Wikipedia

• Hyperbolic partial differential equation — In mathematics, a hyperbolic partial differential equation is usually a second order partial differential equation (PDE) of the form :A u {xx} + 2 B u {xy} + C u {yy} + D u x + E u y + F = 0 with: det egin{pmatrix} A B B C end{pmatrix} = A C B^2 …   Wikipedia

• Diffusion equation — The diffusion equation is a partial differential equation which describes density fluctuations in a material undergoing diffusion. It is also used to describe processes exhibiting diffusive like behaviour, for instance the diffusion of alleles in …   Wikipedia

• Parametric array — The parametric array is a nonlinear transduction mechanism that generates narrow, nearly sidelobe free beams of low frequency sound, through the mixing and interaction of high frequency sound waves, effectively overcoming the diffraction limit (a …   Wikipedia