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PDE-constrained optimization is a subset of mathematical optimization where at least one of the constraints may be expressed as a partial differential equation. [1] Typical domains where these problems arise include aerodynamics , computational fluid dynamics , image segmentation , and inverse problems . [ 2 ]
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...
Method of lines - the example, which shows the origin of the name of method. The method of lines (MOL, NMOL, NUMOL [1] [2] [3]) is a technique for solving partial differential equations (PDEs) in which all but one dimension is discretized.
The Adomian decomposition method (ADM) is a semi-analytical method for solving ordinary and partial nonlinear differential equations.The method was developed from the 1970s to the 1990s by George Adomian, chair of the Center for Applied Mathematics at the University of Georgia. [1]
Even more generally, there is an important class of elliptic systems which consist of coupled partial differential equations for multiple 'unknown' functions. [6] For example, the Cauchy–Riemann equations from complex analysis can be viewed as a first-order elliptic system for a pair of two-variable functions.
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.. The function is often thought of as an "unknown" that solves the equation, similar to how x is thought of as an unknown number solving, e.g., an algebraic equation like x 2 − 3x + 2 = 0.
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In mathematics, the method of characteristics is a technique for solving partial differential equations.Typically, it applies to first-order equations, though in general characteristic curves can also be found for hyperbolic and parabolic partial differential equation.