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Wyświetlanie 1-15 z 37
Tytuł:
Continuous solutions of iterative equations of infinite order
Autorzy:
Kapica, R.
Morawiec, J.
Powiązania:
https://bibliotekanauki.pl/articles/255177.pdf
Data publikacji:
2009
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
random-valued vector functions
sequences of iterates
iterative equations
continuous solutions
Opis:
Given a probability space (Ω, A, P) and a complete separable metric space X, we consider R continuous and bounded solutions φ: X → R of the equations φ (x) = ∫Ω φ(ƒ(x, ω)) P(dω) and φ(x) = 1 - ∫Ωφ(ƒ(x, ω)) P(dω), assuming that the given function ƒ : X x Ω → X is controlled by a random variable L: Ω → (0, ∞) with -∞ < ∫Ω log L (ω) P (dω) < 0. An application to a refinement type equation is also presented.
Źródło:
Opuscula Mathematica; 2009, 29, 2; 147-155
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on the order of polynomial-like iterative equations
Autorzy:
Draga, Szymon
Powiązania:
https://bibliotekanauki.pl/articles/746204.pdf
Data publikacji:
2016
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
continuous solution
iterate
polynomial-like iterative equation
recurrence relation
Opis:
We show that, under reasonable assumptions, two negative roots can be eliminated from the characteristic equation of a polynomial-like iterative equation. This result gives a new case where we may lower the order of such an equation.
Źródło:
Commentationes Mathematicae; 2016, 56, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solutions with big graph of iterative functional equations of the first order
Autorzy:
Bartłomiejczyk, Lech
Powiązania:
https://bibliotekanauki.pl/articles/965988.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
iterative functional equation
big graph
Opis:
We obtain a result on the existence of a solution with big graph of functional equations of the form g(x,(x),(f(x)))=0 and we show that it is applicable to some important equations, both linear and nonlinear, including those of Abel, Böttcher and Schröder. The graph of such a solution has some strange properties: it is dense and connected, has full outer measure and is topologically big.
Źródło:
Colloquium Mathematicum; 1999, 82, 2; 223-230
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On extension of solutions of a simultaneous system of iterative functional equations
Autorzy:
Matkowski, J.
Powiązania:
https://bibliotekanauki.pl/articles/255855.pdf
Data publikacji:
2009
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
functional equation
simultaneous system of equations
local solution
extension theorem
Opis:
Some sufficient conditions which allow to extend every local solution of a simultaneous system of equations in a single variable of the form φ(x)=h(x, φ[ƒ1(x)],…, φ[ƒm(x)]) φ(x)=H(x,φ[F1(x),…, [Fn(x)]) to a global one are presented. Extensions of solutions of functional equations, both in single and in several variables, play important role (cf. for instance [1-3]).
Źródło:
Opuscula Mathematica; 2009, 29, 4; 415-421
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
New iterative method of solving nonlinear equations in fluid mechanics
Autorzy:
Palivets, M.
Andreev, E.
Bakshtanin, A.
Benin, D.
Snezhko, V.
Powiązania:
https://bibliotekanauki.pl/articles/2106452.pdf
Data publikacji:
2021
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
trzęsienie ziemi
mechanika płynów
porowatość
Adomian Decomposition Method ADM
earthquake
filtration
fluid mechanics
iterative method
nonlinear fractional partial differential equations
porous medium
Opis:
This paper presents the results of applying a new iterative method to linear and nonlinear fractional partial differential equations in fluid mechanics. A numerical analysis was performed to find an exact solution of the fractional wave equation and fractional Burgers’ equation, as well as an approximate solution of fractional KdV equation and fractional Boussinesq equation. Fractional derivatives of the order are described using Caputo's definition with 01<α≤ or 12<α≤. A comparative analysis of the results obtained using a new iterative method with those obtained by the Adomian decomposition method showed the first method to be more efficient and simple, providing accurate results in fewer computational operations. Given its flexibility and ability to solve nonlinear equations, the iterative method can be used to solve more complex linear and nonlinear fractional partial differential equations.
Źródło:
International Journal of Applied Mechanics and Engineering; 2021, 26, 3; 163--176
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Monotone iterative technique for fractional differential equations with periodic boundary conditions
Autorzy:
Ramirez, J. D.
Vatsala, A. S.
Powiązania:
https://bibliotekanauki.pl/articles/255247.pdf
Data publikacji:
2009
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Riemann-Liouville fractional derivative
monotone method
periodic boundary value problem
Opis:
In this paper we develop Monotone Method using upper and lower solutions for fractional differential equations with periodic boundary conditions. Initially we develop a comparison result and prove that the solution of the linear fractional differential equation with periodic boundary condition exists and is unique. Using this we develop iterates which converge uniformly monotonically to minimal and maximal solutions of the nonlinear fractional differential equations with periodic boundary conditions in the weighted norm.
Źródło:
Opuscula Mathematica; 2009, 29, 3; 289-304
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solutions of Benjamin-Bona-Mahony, modified Camassa-Holm and Degasperis Procesi equations using an iterative method
Autorzy:
Kumar, Manoj
Powiązania:
https://bibliotekanauki.pl/articles/2202030.pdf
Data publikacji:
2022
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
nonlinear Bejamin-Bona-Mahony equation
modified Camassa-Holm equation
modified Degasperis-Procesi equation
Daftardar-Gejji and Jafari method
homotopy perturbation method
Adomian decomposition method
nieliniowe równanie Bejamina-Bony-Mahony'ego
zmodyfikowane równanie Camassy-Holma
zmodyfikowane równanie Degasperisa-Procesiego
metoda Daftardara-Gejji i Jafari
metoda perturbacji homotopii
metoda dekompozycji Adomiana
Opis:
In the present paper, we solve the non-linear Benjamin-Bona-Mahony, modified Camassa-Holm, and Degasperis-Procesi equations using an iterative method introduced by Daftardar-Gejji and Jafari. Results are compared with those obtained by other iterative methods such as the Adomian decomposition method and homotopy perturbation method. It is observed that the proposed method is computationally inexpensive and yields more accurate solutions than the Adomian decomposition method and the homotopy perturbation method.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 3; 59--72
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On some equations y(x) = f(x,y(h(x)+g(y(x))))
Autorzy:
Grande, Zbigniew
Powiązania:
https://bibliotekanauki.pl/articles/729365.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
iterative differential equation
existence and uniqueness theorem
Picard approximation
derivative
(S)-continuity
(S)-path continuity
Opis:
In [4] W. Li and S.S. Cheng prove a Picard type existence and uniqueness theorem for iterative differential equations of the form y'(x) = f(x,y(h(x)+g(y(x)))). In this article I show some analogue of this result for a larger class of functions f (also discontinuous), in which a unique differentiable solution of considered Cauchy's problem is obtained.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2011, 31, 2; 173-182
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Iterative refinement of least squares solutions computed from normal equations
Autorzy:
Kiełbasiński, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/747675.pdf
Data publikacji:
1989
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Iterative methods for linear systems
Opis:
.
It is shown that iterative refinement (using normal equations and exclusively standard floating point arithmetic with relative precision v) yields almost full accuracy of computed solution to regular linear least squares problem, provided some conditions.
Źródło:
Mathematica Applicanda; 1989, 17, 31
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Monotone iterative methods for infinite systems of reaction-diffusion-convection equations with functional dependence
Autorzy:
Brzychczy, S.
Powiązania:
https://bibliotekanauki.pl/articles/255097.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
infinite systems
reaction-diffusion-convection equations
semilinear parabolic differential-functional equations
Volterra functionals
monotone iterative methods
method of upper and lower solutions
Opis:
We consider the Fourier first initial-boundary value problem for an infinite system of semilinear parabolic differential-functional equations of reaction-diffusion-convection type of the form [formula] where [formula] in a bounded cylindrical domain (0, T] x G := D rcup Rm+1. The right-hand sides of the system are Volterra type functionals of the unknown function z. In the paper, we give methods of the construction of the monotone iterative sequences converging to the unique classical solution of the problem considered in partially ordered Banach spaces with various convergence rates of iterations. We also give remarks on monotone iterative methods in connection with numerical methods, remarks on methods for the construction of lower and upper solutions and remarks concerning the possibility of extending these methods to more general parabolic equations. All monotone iterative methods are based on differential inequalities and, in this paper, we use the theorem on weak partial differential-functional inequalities for infinite systems of parabolic equations, the comparison theorem and the maximum principle. A part of the paper is based on the results of our previous papers. These results generalize the results obtained by several authors in numerous papers for finite systems of semilinear parabolic differential equations to encompass the case of infinite systems of semilinear parabolic differential-functional equations. The monotone iterative schemes can be used for the computation of numerical solutions.
Źródło:
Opuscula Mathematica; 2005, 25, 1; 29-99
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 37

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