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Tytuł:
Initial value problems in elasticity
Autorzy:
Leis, Rolf
Powiązania:
https://bibliotekanauki.pl/articles/1361148.pdf
Data publikacji:
1992
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Źródło:
Banach Center Publications; 1992, 27, 1; 277-294
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A verified method for solving piecewise smooth initial value problems
Autorzy:
Auer, E.
Kiel, S.
Rauh, A.
Powiązania:
https://bibliotekanauki.pl/articles/331354.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
interval method
non smooth system
initial value problem
metoda przedziałowa
metoda nie gładka
zagadnienie początkowe
Opis:
In many applications, there is a need to choose mathematical models that depend on non-smooth functions. The task of simulation becomes especially difficult if such functions appear on the right-hand side of an initial value problem. Moreover, solution processes from usual numerics are sensitive to roundoff errors so that verified analysis might be more useful if a guarantee of correctness is required or if the system model is influenced by uncertainty. In this paper, we provide a short overview of possibilities to formulate non-smooth problems and point out connections between the traditional non-smooth theory and interval analysis. Moreover, we summarize already existing verified methods for solving initial value problems with non-smooth (in fact, even not absolutely continuous) right-hand sides and propose a way of handling a certain practically relevant subclass of such systems. We implement the approach for the solver VALENCIA-IVP by introducing into it a specialized template for enclosing the first-order derivatives of non-smooth functions. We demonstrate the applicability of our technique using a mechanical system model with friction and hysteresis. We conclude the paper by giving a perspective on future research directions in this area.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2013, 23, 4; 731-747
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Multigrid method for numerical solution of ordinary differential equations
Autorzy:
Kozakiewicz, J. M.
Mika, J. R.
Powiązania:
https://bibliotekanauki.pl/articles/747463.pdf
Data publikacji:
1992
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Initial value problems
Opis:
.
We consider the initial value problem for systems of ordinary differential equations such that the solution vector can be split into subvectors and each subvector represented as a product of a scalar amplitude and a shape vector which changes slowly with time. The equations for the shape vectors can be solved with much larger time steps than those required for the original equations. The numerical results show that a substantial reduction in the computing time may be achieved
Źródło:
Mathematica Applicanda; 1992, 21, 35
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On initial value problems for a class of first order impulsive differential inclusions
Autorzy:
Benchohra, Mouffak
Boucherif, Abdelkader
Nieto, Juan
Powiązania:
https://bibliotekanauki.pl/articles/729298.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
impulsive initial value problem
set-valued map
condensing map
fixed point
Opis:
We investigate the existence of solutions to first order initial value problems for differential inclusions subject to impulsive effects. We shall rely on a fixed point theorem for condensing maps to prove our results.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2001, 21, 2; 159-171
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Using Shehu integral transform to solve fractional order Caputo type initial value problems
Autorzy:
Qureshi, Sania
Kumar, Prem
Powiązania:
https://bibliotekanauki.pl/articles/122809.pdf
Data publikacji:
2019
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
ordinary differential equations
Laplace transform
Riemann-Liouville integral
równanie różniczkowe zwyczajne
transformata Laplace'a
całka Riemann-Liouville
Opis:
In the present research analysis, linear fractional order ordinary differential equations with some defined condition (s) have been solved under the Caputo differential operator having order α > 0 via the Shehu integral transform technique. In this regard, we have presented the proof of finding the Shehu transform for a classical nth order integral of a piecewise continuous with an exponential nt h order function which leads towards devising a theorem to yield exact analytical solutions of the problems under investigation. Varying fractional types of problems are solved whose exact solutions can be compared with solutions obtained through existing transformation techniques including Laplace and Natural transforms.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 2; 75-83
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Determining the step of integration for the one-step Bobkovs methods
Autorzy:
Szyszkowicz, Mieczysław
Powiązania:
https://bibliotekanauki.pl/articles/748261.pdf
Data publikacji:
1985
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Initial value problems
Automated algorithms
Opis:
.
Consider the class of Bobkov methods for solving the IVP: y′=f(x,y), x[a,b]. Four procedures for finding the step size h are presented. It is shown that these Bobkov methods with automatic stepsize control are faster (i.e. need fewer evaluations of f) than the corresponding Runge-Kutta methods.
Źródło:
Mathematica Applicanda; 1985, 13, 25
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence of minimal and maximal solutions to RL fractional integro-differential initial value problems
Autorzy:
Denton, Z.
Ramirez, J. D.
Powiązania:
https://bibliotekanauki.pl/articles/255901.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Riemann Liouville derivative
integro-differential equation
monotone method
Opis:
In this work we investigate integro-differential initial value problems with Riemann Liouville fractional derivatives where the forcing function is a sum of an increasing function and a decreasing function. We will apply the method of lower and upper solutions and develop two monotone iterative techniques by constructing two sequences that converge uniformly and monotonically to minimal and maximal solutions. In the first theorem we will construct two natural sequences and in the second theorem we will construct two intertwined sequences. Finally, we illustrate our results with an example.
Źródło:
Opuscula Mathematica; 2017, 37, 5; 705-724
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Appendix to the paper "Osgood type conditions for an mth order differential equation"
Autorzy:
Szufla, Stanisław
Powiązania:
https://bibliotekanauki.pl/articles/729294.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
initial value problems
measures of noncompactness
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2001, 21, 1; 149-153
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Randomized and quantum algorithms for solving initial-value problems in ordinary differential equations of order k
Autorzy:
Goćwin, M.
Szczęsny, M.
Powiązania:
https://bibliotekanauki.pl/articles/255063.pdf
Data publikacji:
2008
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
k-th order initial-value problems
randomized computing
quantum computing
optimal algorithms
complexity
Opis:
The complexity of initial-value problems is well studied for systems of equations of first order. In this paper, we study the ε-complexity for initial-value problems for scalar equations of higher order. We consider two models of computation, the randomized model and the quantum model. We construct almost optimal algorithms adjusted to scalar equations of higher order, without passing to systems of first order equations. The analysis of these algorithms allows us to establish upper complexity bounds. We also show (almost) matching lower complexity bounds. The ε-complexity in the randomized and quantum setting depends on the regularity of the right-hand side function, but is independent of the order of equation. Comparing the obtained bounds with results known in the deterministic case, we see that randomized algorithms give us a speed-up by 1/2, and quantum algorithms by 1 in the exponent. Hence, the speed-up does not depend on the order of equation, and is the same as for the systems of equations of first order. We also include results of some numerical experiments which confirm theoretical results.
Źródło:
Opuscula Mathematica; 2008, 28, 3; 247-277
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Laplace-Carson integral transform for exact solutions of non-integer order initial value problems with Caputo operator
Autorzy:
Kumar, Prem
Qureshi, Sania
Powiązania:
https://bibliotekanauki.pl/articles/122736.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
ordinary differential equations
Laplace transform
Riemann-Liouville integral
równanie różniczkowe zwyczajne
transformacja Laplace'a
całka Riemann-Liouville
Opis:
Finding the exact solution to dynamical systems in the field of mathematical modeling is extremely important and to achieve this goal, various integral transforms have been developed. In this research analysis, non-integer order ordinary differential equations are analytically solved via the Laplace-Carson integral transform technique, which is a technique that has not been previously employed to test the non-integer order differential systems. Firstly, it has proved that the Laplace-Carson transform for n-times repeated classical integrals can be computed by dividing the Laplace-Carson transform of the underlying function by n-th power of a real number p which later helped us to present a new result for getting the Laplace-Carson transform for d-derivative of a function under the Caputo operator. Some initial value problems based upon Caputo type fractional operator have been precisely solved using the results obtained thereof.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 57-66
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Laplace-Carson integral transform for exact solutions of non-integer order initial value problems with Caputo operator
Autorzy:
Kumar, Prem
Qureshi, Sania
Powiązania:
https://bibliotekanauki.pl/articles/1839810.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
ordinary differential equations
Laplace transform
Riemann-Liouville integral
równanie różniczkowe zwyczajne
transformacja Laplace'a
całka Riemann-Liouville
Opis:
Finding the exact solution to dynamical systems in the field of mathematical modeling is extremely important and to achieve this goal, various integral transforms have been developed. In this research analysis, non-integer order ordinary differential equations are analytically solved via the Laplace-Carson integral transform technique, which is a technique that has not been previously employed to test the non-integer order differential systems. Firstly, it has proved that the Laplace-Carson transform for n-times repeated classical integrals can be computed by dividing the Laplace-Carson transform of the underlying function by n-th power of a real number p which later helped us to present a new result for getting the Laplace-Carson transform for d-derivative of a function under the Caputo operator. Some initial value problems based upon Caputo type fractional operator have been precisely solved using the results obtained thereof.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 57-66
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new numerical technique for solving fractional Bratu’s initial value problems in the Caputo and Caputo-Fabrizio sense
Autorzy:
Khalouta, Ali
Kadem, Abdelouahab
Powiązania:
https://bibliotekanauki.pl/articles/1839797.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
fractional Bratu’s initial value problem
Caputo fractional derivative
Caputo-Fabrizio fractional derivative
natural transform method
Adomian decomposition method
ułamkowa pochodna Caputo
ułamkowa pochodna Caputo-Fabrizio
metoda transformacji naturalnej
metoda dekompozycji Adomiana
Opis:
The purpose of this paper is to propose a new numerical technique called the natural decomposition method (NDM) for solving fractional Bratu’s initial value problems (FBIVP) in the Caputo and Caputo-Fabrizio sense. The NDM is a combined form of the natural transform method and the Adomian decomposition method. The numerical example is provided in order to validate the efficiency and reliability of the proposed method. The obtained results reveal that the proposed method is a very efficient and simple tool for solving fractional differential equations.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 43-56
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new numerical technique for solving fractional Bratu’s initial value problems in the Caputo and Caputo-Fabrizio sense
Autorzy:
Khalouta, Ali
Kadem, Abdelouahab
Powiązania:
https://bibliotekanauki.pl/articles/122619.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
fractional Bratu’s initial value problem
Caputo fractional derivative
Caputo-Fabrizio fractional derivative
natural transform method
Adomian decomposition method
ułamkowa pochodna Caputo
ułamkowa pochodna Caputo-Fabrizio
metoda transformacji naturalnej
metoda dekompozycji Adomiana
Opis:
The purpose of this paper is to propose a new numerical technique called the natural decomposition method (NDM) for solving fractional Bratu’s initial value problems (FBIVP) in the Caputo and Caputo-Fabrizio sense. The NDM is a combined form of the natural transform method and the Adomian decomposition method. The numerical example is provided in order to validate the efficiency and reliability of the proposed method. The obtained results reveal that the proposed method is a very efficient and simple tool for solving fractional differential equations.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 43-56
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Two-step Hybrid Block Method for the Numerical Integration of Higher Order Initial Value Problems of Ordinary Differential Equations
Autorzy:
Osa, Adoghe Lawrence
Olaoluwa, Omole Ezekiel
Powiązania:
https://bibliotekanauki.pl/articles/1075837.pdf
Data publikacji:
2019
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Block method
Collocation
Fourth order
Higher Order
Hybrid
approximate solutions
power series
symmetry
zero stability
Opis:
In this paper, a two-step implicit hybrid block multistep method is proposed for the approximate solution of higher order ordinary differential equations with a specification of fourth order. The study provides the use of both collocation and interpolation techniques to obtain the schemes. Direct form of power series is used as basis function for approximation solution. An order eight symmetric and zero-stable method is obtained. To implement our method, predictors of the same order of accuracy as the main method were developed using Taylor’s series algorithm. This implementation strategy is found to be efficient and more accurate as the result has shown in the numerical experiments. The result obtained confirmed the superiority of our method over existing methods.
Źródło:
World Scientific News; 2019, 118; 236-250
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A singular initial value problem for second and third order differential equations
Autorzy:
Mydlarczyk, Wojciech
Powiązania:
https://bibliotekanauki.pl/articles/967100.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
initial value problems for second and third order differential equations
blowing up solutions
Źródło:
Colloquium Mathematicum; 1995, 68, 2; 249-257
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On an Euler-like method with exponential correction for initial-value problems
O analogonie metody Eulera z poprawką wykładniczą dla zadań początkowych
Autorzy:
Pokora, Teresa
Ząbek, Ś.
Powiązania:
https://bibliotekanauki.pl/articles/742322.pdf
Data publikacji:
1972
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Źródło:
Applicationes Mathematicae; 1972-1973, 13, 2; 255-259
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Initial-boundary value problems for impulsive parabolic functional differential equations
Autorzy:
Bainov, D.
Kamont, Zdzisław
Minchev, E.
Powiązania:
https://bibliotekanauki.pl/articles/1339288.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
initial-boundary value problems
impulsive parabolic equations
Opis:
Theorems on differential inequalities generated by an initial-boundary value problem for impulsive parabolic functional differential equations are considered. Comparison results implying uniqueness criteria are proved.
Źródło:
Applicationes Mathematicae; 1996-1997, 24, 1; 1-15
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A singular initial value problem for the equation $u^{(n)}(x) = g(u(x))$
Autorzy:
Mydlarczyk, Wojciech
Powiązania:
https://bibliotekanauki.pl/articles/1294503.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
singular initial value problems for ordinary differential equations
Volterra type integral equations
blowing up solutions
Opis:
We consider the problem of the existence of positive solutions u to the problem $u^{(n)}(x) = g(u(x))$,
$u(0) = u'(0) = ... = u^{(n-1)}(0) = 0$ (g ≥ 0,x > 0, n ≥ 2). It is known that if g is nondecreasing then the Osgood condition $∫₀^δ 1/s [s/g(s)]^{1/n} ds < ∞$ is necessary and sufficient for the existence of nontrivial solutions to the above problem. We give a similar condition for other classes of functions g.
Źródło:
Annales Polonici Mathematici; 1998, 68, 2; 177-189
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-25 z 42

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