A method for approximately solving non-linear operator
equations. It consists of generalizing the equation to be solved, <img align="absmidd
If the
difference <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/l
10 KB (1,328 words) - 17:04, 7 February 2011
...nary differential equations with deviated arguments, ordinary differential equations with deviating arguments''
Ordinary differential equations connecting the argument, the unknown function and its derivatives generally taken for different values of the argument. Examp
27 KB (3,819 words) - 16:54, 7 February 2011
...athematical physics where the boundaries of the working regions are moving and undergo considerable deformations. A substantial part of an algorithm for h
...the cells (the enumeration is analogous to that of matrix elements by rows and columns).
5 KB (759 words) - 10:59, 16 April 2014
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...a12]]], [[#References|[a13]]], [[#References|[a14]]], [[#References|[a2]]] and the numerous references therein).
15 KB (2,182 words) - 12:41, 23 February 2024
...0107360 Boundary value problem, numerical methods for partial differential equations
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...transport equation (cf. [[Transport equations, numerical methods|Transport equations, numerical methods]])
4 KB (433 words) - 08:28, 6 June 2020
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from above and from below. An estimate from above is an inequality of the form $ a \leq
8 KB (1,164 words) - 08:27, 6 June 2020
...rd "system" in their names, such as systems analysis, system-technology, and general systems theory, among others.
...s to the description of complex systems are united by a common methodology and a common object of study.
4 KB (532 words) - 17:22, 7 February 2011
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in the problem of an extremum for the functional
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$#C+1 = 201 : ~/encyclopedia/old_files/data/D031/D.0301730 Difference scheme, variational
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22 KB (3,256 words) - 17:33, 5 June 2020
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...ving problems of optimal control with constraints on the phase coordinates and control functions, based on variation in the state space (see [[#References
6 KB (898 words) - 17:24, 31 December 2020
$#C+1 = 153 : ~/encyclopedia/old_files/data/F042/F.0402060 Functional equation
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19 KB (2,803 words) - 19:40, 5 June 2020
$#C+1 = 201 : ~/encyclopedia/old_files/data/F042/F.0402070 Functional equation, methods of solution of a
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23 KB (3,277 words) - 19:16, 16 January 2024
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and range of values in a Banach space $ Y $.
6 KB (956 words) - 12:55, 20 March 2023
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...e to a solution of the given equation. The stability problem of functional equations originates from such a fundamental question.
12 KB (1,800 words) - 19:48, 6 February 2024
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A method for solving functional equations of the type:
8 KB (1,085 words) - 08:29, 6 June 2020
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...e, two problems are usually studied: the [[Cauchy problem|Cauchy problem]] and the [[Mixed problem|mixed problem]].
6 KB (798 words) - 05:40, 19 March 2022
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...ense, this name, adopted also by A.L. Cauchy, was used in the 19th century and in the 20th century (cf. [[#References|[a2]]], [[#References|[a3]]], [[#Ref
6 KB (957 words) - 06:42, 26 March 2023
...mula]] [[#References|[a1]]], [[Spline interpolation|spline interpolation]] and Fourier transformation (cf. [[Fourier transform|Fourier transform]]) [[#Ref
...fferential equations. The complete error analysis of the finite difference and finite volume schemes in [[#References|[a9]]] is based on the Bramble–Hil
11 KB (1,716 words) - 17:52, 3 January 2021
...m of analytical expressions are only known for a few types of differential equations.
...f the oldest methods for the approximate solution of ordinary differential equations is their expansion into a Taylor series. In this method the solution of an
32 KB (4,604 words) - 16:55, 7 February 2011
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...the study of many classes of partial and functional differential equations and has solved problems that had been left open by the previous classical metho
8 KB (1,236 words) - 17:03, 1 July 2020
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...s it is typical to assume that the solution of the original problem exists and has sufficiently many derivatives. Because of the absence of other assumpti
17 KB (2,540 words) - 19:55, 12 January 2024
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...f the original problem, but such a discretization is nevertheless implicit and is realized relative to a known model.
19 KB (2,657 words) - 14:54, 7 June 2020
...ue of its derivative, at a given point of the extremal. In the case of the functional
and let $ X ^{*} $
7 KB (975 words) - 22:37, 28 January 2020
...old_files/data/B017/B.0107380 Boundary value problem, partial differential equations
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11 KB (1,579 words) - 06:29, 30 May 2020
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...ly related to those of a [[Generalized derivative|generalized derivative]] and a [[Generalized function|generalized function]]. The concept of a generaliz
7 KB (1,006 words) - 19:41, 5 June 2020
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...terpolation|interpolation]] of functions. The interpolation of functionals and operators is also widely used in constructing numerical methods.
26 KB (3,882 words) - 22:13, 5 June 2020
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...tions. The best known of these are the [[Löwner equation|Löwner equation]] and the Löwner–Kufarev equation. In the discrete case — for lattice domain
8 KB (1,168 words) - 20:13, 12 January 2024
...rder in function spaces makes it possible to study within the framework of
functional analysis problems that are essentially connected with inequalities between
...opediaofmath.org/legacyimages/s/s084/s084260/s08426022.png" /> is a wedge,
and every wedge with vertex at the origin generates a quasi-order in <img align
43 KB (5,981 words) - 17:13, 2 May 2020
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a minimum of a functional, eigen values and eigen vectors of an equation $ A u = \lambda u $,
8 KB (1,124 words) - 11:46, 17 June 2020
$#C+1 = 202 : ~/encyclopedia/old_files/data/T093/T.0903900 Transport equations, numerical methods
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17 KB (2,415 words) - 09:04, 13 January 2024
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...mation is functionally parametrized by a pair of solutions of the equation and the transform vanishes if the solutions coincide.
14 KB (2,023 words) - 17:02, 1 July 2020
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...ad influences on many parts of mathematics and different areas of sciences and technology ([[#References|[a4]]], [[#References|[a7]]], [[#References|[a8]]
7 KB (1,001 words) - 16:57, 1 July 2020
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Iteration methods for the solution of non-linear equations.
20 KB (2,830 words) - 19:25, 9 January 2024
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...ight makes it possible to enlarge or restrict ordinary non-weighted normed and semi-normed function spaces consisting of functions with infinite ordinary
9 KB (1,435 words) - 08:13, 13 January 2024
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...tic aspects), depending on input functions or parameters, called controls, and usually subject to constraints. The sought controls, as well as the realiza
21 KB (3,161 words) - 08:04, 6 June 2020
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A system of ordinary differential equations in the numerical solution of which by explicit methods of Runge–Kutta or
30 KB (4,292 words) - 05:40, 24 February 2022
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...statistical models for vertical-heterogeneous random fields of turbulence and [[Internal waves|internal waves]] (cf. also [[Turbulence, mathematical prob
13 KB (1,880 words) - 08:03, 6 June 2020
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...respective boundary value problem. In direct methods, the extremum of the functional is found directly. The optimization methods thus employed are a development
23 KB (3,462 words) - 08:27, 6 June 2020
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defined and acting on a closed subset $ G $
15 KB (2,235 words) - 08:13, 6 June 2020
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...ing them, to an examination of simpler algebraic problems. The development and systematic use of operational calculus began with the work of O. Heaviside
12 KB (1,635 words) - 14:54, 7 June 2020
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is considered to be fixed for the given quadrature formula and is called the weight function; the function $ f ( x) $
11 KB (1,719 words) - 01:56, 4 January 2022
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...atics that are applied to find the extrema (maxima or minima) of functions and functionals.
22 KB (3,158 words) - 19:38, 5 June 2020
...everal classes of functions that arise in the solution of both theoretical and applied problems in various branches of mathematics.
...ons of mathematical physics, which arise when solving partial differential equations by the
7 KB (905 words) - 12:54, 1 May 2023
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...ymplectic manifolds, Hamiltonian vector fields, symplectic diffeomorphisms and Lagrangean submanifolds.
15 KB (2,211 words) - 07:18, 15 February 2024
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A branch of modern computational mathematics, devoted to the design and investigation of methods which allow one to find an approximate solution, w
20 KB (2,838 words) - 19:21, 13 January 2024
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and of the strain tensor $ \epsilon _ {ij} ( x, t) $,
28 KB (4,176 words) - 05:30, 19 March 2022
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...nti-holomorphic involution, cf. also [[Riemann surface|Riemann surface]]), and with the theory of multi-dimensional systems. The theory of operator vessel
24 KB (3,136 words) - 20:00, 24 November 2023
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and the law of motion of the dividing boundary $ \xi = \xi ( t) $(
12 KB (1,620 words) - 08:23, 6 June 2020
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and $ A _ {1} ( t) $,
32 KB (4,803 words) - 17:49, 6 January 2024