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  2. First-order upwind scheme - Wikipedia

    en.wikipedia.org/wiki/Upwind_scheme

    A Taylor series analysis of the upwind scheme discussed above will show that it is first-order accurate in space and time. Modified wavenumber analysis shows that the first-order upwind scheme introduces severe numerical diffusion /dissipation in the solution where large gradients exist due to necessity of high wavenumbers to represent sharp ...

  3. False diffusion - Wikipedia

    en.wikipedia.org/wiki/False_diffusion

    However, for large Peclet numbers (generally > 2) this approximation gave inaccurate results. It was recognized independently by several investigators [1] [2] that the less expensive but only first order accurate upwind scheme can be employed but that this scheme produces results with false diffusion for multidimensional cases. Many new schemes ...

  4. Ordered pair - Wikipedia

    en.wikipedia.org/wiki/Ordered_pair

    Let (,) and (,) be ordered pairs. Then the characteristic (or defining) property of the ordered pair is: (,) = (,) = =.. The set of all ordered pairs whose first entry is in some set A and whose second entry is in some set B is called the Cartesian product of A and B, and written A × B.

  5. Godunov's scheme - Wikipedia

    en.wikipedia.org/wiki/Godunov's_scheme

    Following the classical finite volume method framework, we seek to track a finite set of discrete unknowns, = / + / (,) where the / = + (/) and = form a discrete set of points for the hyperbolic problem: + (()) =, where the indices and indicate the derivatives in time and space, respectively.

  6. MUSCL scheme - Wikipedia

    en.wikipedia.org/wiki/MUSCL_scheme

    Shows the analytical solution along with a simulation based upon a first order upwind spatial discretization scheme. We will consider the fundamentals of the MUSCL scheme by considering the following simple first-order, scalar, 1D system, which is assumed to have a wave propagating in the positive direction,

  7. Tarski's axioms - Wikipedia

    en.wikipedia.org/wiki/Tarski's_axioms

    The Axiom Schema of Continuity assures that the ordering of points on a line is complete (with respect to first-order definable properties). As was pointed out by Tarski, this first-order axiom schema may be replaced by a more powerful second-order Axiom of Continuity if one allows for variables to refer to arbitrary sets of points. The ...

  8. Base pair - Wikipedia

    en.wikipedia.org/wiki/Base_pair

    An unnatural base pair (UBP) is a designed subunit (or nucleobase) of DNA which is created in a laboratory and does not occur in nature. DNA sequences have been described which use newly created nucleobases to form a third base pair, in addition to the two base pairs found in nature, A-T (adenine – thymine) and G-C (guanine – cytosine).

  9. Hilbert's axioms - Wikipedia

    en.wikipedia.org/wiki/Hilbert's_axioms

    Removing five axioms mentioning "plane" in an essential way, namely I.4–8, and modifying III.4 and IV.1 to omit mention of planes, yields an axiomatization of Euclidean plane geometry. Hilbert's axioms, unlike Tarski's axioms, do not constitute a first-order theory because the axioms V.1–2 cannot be expressed in first-order logic.

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