...10/b1100108.png" />) are of no use for an appropriate characterization and
analysis of methods which are able to efficiently integrate a stiff problem. Thus th
...a coefficients entailing B-stability was derived ( "algebraic stability in
numerical analysisalgebraic stability" ). The notion of <img align="absmiddle" border
11 KB (1,517 words) - 17:23, 7 February 2011
...lign="top">[4]</TD> <TD valign="top"> A.A. Samarskii, E.S. Nikolaev, "Numerical methods for grid equations" , '''1–2''' , Birkhäuser (1989) (Translate
.../TD> <TD valign="top"> U.M. Ascher, R.M.M. Mattheij, R.D. Russell, "Numerical solution for boundary value problems for ordinary differential equations" ,
7 KB (1,036 words) - 19:36, 5 June 2020
...solved, this system has the form of a recurrence relation here. For other numerical methods, see [[#References|[a1]]]. Volterra equations of the first kind are
...<TD valign="top"> A.E. Taylor, D.C. Lay, "Introduction to functional analysis" , Wiley (1980)</TD></TR></table>
13 KB (1,966 words) - 08:28, 6 June 2020
A very simple finite-difference method for the numerical solution of an ordinary differential equation. Let a differential equation
The numerical algorithm of the Euler method can easily be programmed on a computer.
6 KB (877 words) - 19:38, 5 June 2020
...see [[Multi-dimensional statistical analysis|Multi-dimensional statistical analysis]]). If the results of observations $ X _ {1} \dots X _ {n} $
degrees of freedom. This fact forms the basis of the [[Hotelling test]]. For numerical calculations one uses tables of the [[Beta-distribution|beta-distribution]]
4 KB (517 words) - 19:08, 26 May 2024
...on fluctuations [[#References|[a1]]]. According to such a linear stability
analysis, all long wavelength concentration fluctuations with wavelengths exceeding
The linear stability
analysis of (a1) yields, writing <img align="absmiddle" border="0" src="https://www.
11 KB (1,535 words) - 17:13, 7 February 2011
...ferences|[a3]]] and J. Douglas [[#References|[a1]]] as a technique for the numerical solution of elliptic and parabolic differential equations (cf. [[Elliptic p
...valign="top">[a4]</TD> <TD valign="top"> R.S. Varga, "Matrix iterative analysis" , Prentice-Hall (1962)</TD></TR></table>
5 KB (654 words) - 01:55, 21 January 2022
...Therefore for the solution of these problems, alongside analytic methods, numerical simulation on computers is widely used.
...ithms and programs for the computer realization of the discrete models, an analysis of the sensitivity of the model to variations of the parameters, an estimat
15 KB (2,159 words) - 17:08, 7 February 2011
...iven exactly and is small or has special structure. On the other hand, the numerical computation of the Jordan form of a numerically given matrix is an ill-pose
For recent (1998) surveys of algorithms for numerical linear algebra problems, see [[#References|[a2]]], [[#References|[a3]]], [[
10 KB (1,478 words) - 17:02, 1 July 2020
...ncyclopedia/old_files/data/M065/M.0605140 Multi\AAhdimensional statistical analysis,
''multivariate statistical analysis''
27 KB (3,850 words) - 14:44, 7 June 2020
is ensured under the conditions that the numerical realization of the operations $ A _ {k} u ^ {k} $,
...gn="top">[4]</TD> <TD valign="top"> N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
8 KB (1,124 words) - 11:46, 17 June 2020
...s heuristic principle means that "if one has an important and interesting numerical algorithm, then there is a good chance that its semi-ring analogues are imp
...bi and generalized Bellman equations, cf. [[Idempotent analysis|Idempotent analysis]]) deal with the corresponding finite-dimensional (or finite) "linear appr
7 KB (1,079 words) - 20:39, 16 November 2023
$#C+1 = 49 : ~/encyclopedia/old_files/data/L057/L.0507480 Laplace equation, numerical methods
...elliptic type (see [[#References|[1]]], [[#References|[2]]]) comprise many numerical methods for the Laplace equation. The specific character of the Laplace equ
9 KB (1,360 words) - 13:02, 13 January 2024
...go far beyond approximation considerations, as they appear to have a nice numerical stability (see [[Difference schemes, theory of|Difference schemes, theory o
...nomial spline spaces have been studied in [[#References|[a10]]]. A general analysis of projection methods (of which collocation is a special case) for the solu
12 KB (1,710 words) - 19:39, 18 January 2024
...s to numerical [[Quadrature|quadrature]] and to collocation methods in the numerical solution of functional equations.
...). Error estimation by extended interpolation is an important tool for the numerical approximation of linear functionals.
6 KB (756 words) - 20:24, 5 December 2023
...gn="top">[1]</TD> <TD valign="top"> N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
...[a1]</TD> <TD valign="top"> F.B. Hildebrand, "Introduction to numerical analysis" , Dover, reprint (1987) pp. 275ff</TD></TR><TR><TD valign="top">[a2]</TD
6 KB (778 words) - 14:32, 13 January 2024
In the case of formulas for numerical integration, often the coordinates of the nodes of integration stand out as
...gn="top">[2]</TD> <TD valign="top"> N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
4 KB (621 words) - 11:59, 12 August 2014
...dimensional quantities) have the same numerical values (see [[Dimensional analysis]]). The converse conclusion is also correct, i.e. if all the corresponding
Dimensional analysis and similarity theory are closely related and are used in experiments with
10 KB (1,521 words) - 19:59, 4 January 2024
.../encyclopedia/old_files/data/L059/L.0509110 Linear boundary value problem, numerical methods
...sufficiently many derivatives. Because of the absence of other assumptions numerical methods differ in their universality.
17 KB (2,540 words) - 19:55, 12 January 2024
<TR><TD valign="top">[a4]</TD> <TD valign="top"> J.M. Ortéga, "Numerical analysis" , Acad. Press (1972) {{MR|0403154}} {{ZBL|0248.65001}} </TD></TR>
..."top">[a1]</TD> <TD valign="top"> C.E. Fröberg, "Introduction to numerical analysis, theory and applications" , Benjamin/Cummings (1985)</TD></TR>
7 KB (1,025 words) - 22:14, 5 June 2020