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Reduction of order (or d’Alembert reduction) is a technique in mathematics for solving second-order linear ordinary differential equations. It is employed when one solution is known and a second linearly independent solution is desired. The method also applies to n -th order equations. In this case the ansatz will yield an (n −1)-th order ...
Formal definitions. Formally, a binary relation (→) on the set of terms is called a rewrite relation if it is closed under contextual embedding and under instantiation; formally: if l → r implies u [ l σ] p → u [ r σ] p for all terms l, r, u, each path p of u, and each substitution σ. If (→) is also irreflexive and transitive, then ...
A measure of disorder in the universe or of the unavailability of the energy in a system to do work. [7] Entropy and disorder also have associations with equilibrium. [8] Technically, entropy, from this perspective, is defined as a thermodynamic property which serves as a measure of how close a system is to equilibrium—that is, to perfect ...
In numerical mathematics, Beam and Warming scheme or Beam–Warming implicit scheme introduced in 1978 by Richard M. Beam and R. F. Warming, [1][2] is a second order accurate implicit scheme, mainly used for solving non-linear hyperbolic equations. It is not used much nowadays.
Second-order logic. In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. [1] Second-order logic is in turn extended by higher-order logic and type theory. First-order logic quantifies only variables that range over individuals (elements of the domain of discourse ...
Second-order cybernetics. Second-order cybernetics, also known as the cybernetics of cybernetics, is the recursive application of cybernetics to itself and the reflexive practice of cybernetics according to such a critique. It is cybernetics where "the role of the observer is appreciated and acknowledged rather than disguised, as had become ...
Second-order arithmetic. In mathematical logic, second-order arithmetic is a collection of axiomatic systems that formalize the natural numbers and their subsets. It is an alternative to axiomatic set theory as a foundation for much, but not all, of mathematics. A precursor to second-order arithmetic that involves third-order parameters was ...
Weakened weak form. Weakened weak form (or W2 form) [1] is used in the formulation of general numerical methods based on meshfree methods and/or finite element method settings. These numerical methods are applicable to solid mechanics as well as fluid dynamics problems.