$#C+1 = 31 : ~/encyclopedia/old_files/data/I052/I.0502080 Interval analysis
A theory intended for the calculation of rounding errors of calculations on numerical computers. Since not all numbers can be represented exactly in a computer w
5 KB (677 words) - 22:13, 5 June 2020
[[Category:Numerical analysis and scientific computing]]
1 KB (217 words) - 18:54, 19 October 2014
...tandard procedure is usually applied to the use of mathematical methods in numerical calculations on a computer (computational mathematics, mathematical statist
...]</TD> <TD valign="top"> V.V. Voevodin, O.B. Arushanyan, , ''Numerical Analysis in FORTRAN'' , Moscow (1979) pp. 73–84</TD></TR><TR><TD valign="top">[2
3 KB (372 words) - 17:12, 7 February 2011
...htarrow \mathbf{C} ^ { n }$, is concerned with the question of whether the numerical discretization inherits the dynamic properties of the differential equation
...solutions is a non-increasing function of $x$. Let $y_1$, $z_1$ denote the numerical solutions after one step of size $h$ with initial values $y _ { 0 }$, $z_0$
9 KB (1,275 words) - 17:43, 1 July 2020
...s for the numerical integration (cf. [[Integration, numerical|Integration, numerical]]) of diffusion problems, introduced by J. Crank and P. Nicolson [[#Referen
and numerical initial condition
14 KB (2,138 words) - 08:45, 28 January 2024
are the numerical parameters of the method. If $ \epsilon ^ {k} = u - u ^ {k} $,
...tor equations, and polynomials deviating least from zero" , ''Mathematical analysis and related problems in mathematics'' , Novosibirsk (1978) pp. 89–108
16 KB (2,300 words) - 19:29, 17 January 2024
...rete mathematics and discrete analysis. In what follows the term "discrete analysis" is understood in the wide meaning of the word, including discrete mathemat
As distinct from discrete analysis, classical mathematics deals mainly with continuous objects. The choice bet
9 KB (1,264 words) - 16:56, 15 April 2012
...p">[a5]</TD> <TD valign="top"> P.J. Davis, P. Rabinowitz, "Methods of numerical integration" , Acad. Press (1984)</TD></TR></table>
3 KB (420 words) - 16:58, 14 February 2020
...numerical methods. If the integrand $f$ is given by function values, only numerical methods of the form
.... If adaptive information is superior to non-adaptive information, then an analysis of the trade-off between using adaptive or non-adaptive information on a pa
4 KB (650 words) - 15:07, 14 February 2020
...)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top"> W.E. Milne, "Numerical solution of differential equations" , Dover, reprint (1970)</TD></TR></tab
4 KB (538 words) - 17:45, 20 January 2022
...gn="top">[5]</TD> <TD valign="top"> N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
...[a4]</TD> <TD valign="top"> F.B. Hildebrand, "Introduction to numerical analysis" , Dover, reprint (1987) pp. Chapt. 8 {{MR|0895822}} {{ZBL|0641.65001}}
4 KB (605 words) - 08:02, 6 June 2020
...e form (2), (3) are already implicit. This complicates significantly their numerical implementation: The values $ k _ {n} $,
The approaches to the construction of numerical methods considered above for equations of type (1) can be extended to ordin
9 KB (1,315 words) - 20:04, 15 January 2024
...ign="top"|{{Ref|Ba}}||valign="top"| N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations", MIR (1977) (Translated from R
...{Ref|KaAk}}||valign="top"| L.V. Kantorovich, G.P. Akilov, "Functional analysis", Pergamon (1982) (Translated from Russian) {{MR|0664597}} {{ZBL|0484.4
3 KB (519 words) - 19:10, 6 April 2012
...d in some way with the existence of an invariant structure (see [[Harmonic analysis, abstract]]), when they are eigen functions of the [[Laplace–Beltrami equ
...ory (see [[#References|[6]]] and [[#References|[7]]]) and in the theory of numerical integration (see [[#References|[8]]]).
4 KB (575 words) - 20:24, 20 December 2016
$#C+1 = 73 : ~/encyclopedia/old_files/data/I051/I.0501430 Integral equations, numerical methods
is a numerical parameter and $ K ( x , s ) $
12 KB (1,747 words) - 13:26, 14 January 2022
...op"> W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, "Numerical recipes" , Cambridge Univ. Press (1986) pp. 105ff</TD></TR>
3 KB (476 words) - 16:30, 29 March 2024
...attice points are also of importance in crystallography, coding, numerical analysis, analytic number theory, Diophantine approximation, computational geometry,
2 KB (239 words) - 19:03, 2 October 2016
...[a2]</TD> <TD valign="top"> F.B. Hildebrand, "Introduction to numerical analysis" , McGraw-Hill (1974)</TD></TR></table>
3 KB (490 words) - 17:39, 14 December 2020
|valign="top"|{{Ref|Ba}}||valign="top"| N.S. Bakhvalov, "Numerical methods: analysis, algebra, ordinary differential equations" , MIR (1977) (Translated from
1 KB (234 words) - 21:21, 15 July 2012
...</TD> <TD valign="top"> N.S. Bakhvalov, "On an estimate of the error at numerical integration of differential equations by Adams' extrapolation method" ''Do
...d-held programmable calculator" G.H. Golub (ed.) , ''Studies in numerical analysis'' , Math. Assoc. Amer. (1984) pp. 199–242</TD></TR></table>
6 KB (888 words) - 21:01, 4 April 2020