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Tytuł:
A New Computational Method Based on Laguerre Polynomials for Solving Certain Nonlinear Partial Integro Differential Equations
Autorzy:
Gürbüz, B.
Sezer, M.
Powiązania:
https://bibliotekanauki.pl/articles/1031188.pdf
Data publikacji:
2017-09
Wydawca:
Polska Akademia Nauk. Instytut Fizyki PAN
Tematy:
nonlinear partial integro-differential equations
Laguerre polynomials
matrix and collocation methods
error estimations
Opis:
In this study, we consider some nonlinear partial integro-differential equations. Most of these equations are used as mathematical models in many problems of physics, biology, chemistry, engineering, and in other areas. Our main purpose is to propose a new numerical method based on the Laguerre and Taylor polynomials, called matrix collocation method, for the numerical solution of the mentioned nonlinear equations under the initial or boundary conditions. To show the effectiveness of this approach, some examples along with error estimations are illustrated by tables and figures.
Źródło:
Acta Physica Polonica A; 2017, 132, 3; 561-563
0587-4246
1898-794X
Pojawia się w:
Acta Physica Polonica A
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A nonlocal coagulation-fragmentation model
Autorzy:
Lachowicz, Mirosław
Wrzosek, Dariusz
Powiązania:
https://bibliotekanauki.pl/articles/1208218.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
integro-differential equations
diffusion
coagulation
nonlocal interaction
fragmentation
kinetic models
Opis:
A new nonlocal discrete model of cluster coagulation and fragmentation is proposed. In the model the spatial structure of the processes is taken into account: the clusters may coalesce at a distance between their centers and may diffuse in the physical space Ω. The model is expressed in terms of an infinite system of integro-differential bilinear equations. We prove that some results known in the spatially homogeneous case can be extended to the nonlocal model. In contrast to the corresponding local models the analysis can be carried out in the $L_1(Ω)$ setting. Our purpose is to study global (in time) existence, mass conservation and well-posedness of the model.
Źródło:
Applicationes Mathematicae; 2000, 27, 1; 45-66
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence and convergence results for Caputo fractional Volterra integro-differential equations
Autorzy:
Hamoud, A. A.
Bani Issa, M. Sh.
Ghadle, K. P.
Abdulghani, M.
Powiązania:
https://bibliotekanauki.pl/articles/2052432.pdf
Data publikacji:
2018
Wydawca:
Politechnika Rzeszowska im. Ignacego Łukasiewicza. Oficyna Wydawnicza
Tematy:
homotopy analysis method
Caputo fractional derivative
Volterra integro-differential equation
approximate solution
homotopijna metoda analizy
pochodna ułamkowa Caputo
równanie różniczkowe Volterry
rozwiązanie przybliżone
Opis:
In this article, homotopy analysis method is successfully applied to find the approximate solution of Caputo fractional Volterra integro-differential equation. The reliability of the method and reduction in the size of the computational work give this method a wider applicability. Also, the behavior of the solution can be formally determined by analytical approximate. Moreover, we proved the existence and convergence of the solution. Finally, an example is included to demonstrate the validity and applicability of the proposed technique.
Źródło:
Journal of Mathematics and Applications; 2018, 41; 109-121
1733-6775
2300-9926
Pojawia się w:
Journal of Mathematics and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space
Autorzy:
Almalahi, Mohammed A.
Panchal, Satish K.
Powiązania:
https://bibliotekanauki.pl/articles/1797178.pdf
Data publikacji:
2020-07-20
Wydawca:
Uniwersytet Pedagogiczny im. Komisji Edukacji Narodowej w Krakowie
Tematy:
ψ-Hilfer fractional derivative
Mönch fixed point theorem
Eα-Ulam-Hyers stability
δ-approximate solution
Opis:
In this article we present the existence and uniqueness results for fractional integro-differential equations with ψ-Hilfer fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Mönch fixed point theorem and the Banach fixed point theorem. Furthermore, we discuss $E_{α}$-Ulam-Hyers stability of the presented problem. Also, we use the generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of the δ-approximate solution.
Źródło:
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica; 2020, 19; 171-192
2300-133X
Pojawia się w:
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hybrid fractional integro-differential inclusions
Autorzy:
Ntouyas, Sotiris
Laoprasittichok, Sorasak
Tariboon, Jessada
Powiązania:
https://bibliotekanauki.pl/articles/729621.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
fractional differential equations
hybrid differential inclusions
fixed point theorems
Opis:
In this paper we study an existence result for initial value problems for hybrid fractional integro-differential inclusions. A hybrid fixed point theorem for a sum of three operators due to Dhage is used. An example illustrating the obtained result is also presented.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2015, 35, 2; 151-164
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Integro-differential equations on time scales with Henstock-Kurzweil delta integrals
Autorzy:
Sikorska-Nowak, Aneta
Powiązania:
https://bibliotekanauki.pl/articles/729234.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
integro-differential equations
nonlinear Volterra integral equation
time scales
Henstock-Kurzweil delta integral
HL delta integral
Banach space
fixed point
measure of noncompactness
Carathéodory solutions
Opis:
In this paper we prove existence theorems for integro - differential equations
$x^Δ (t) = f(t,x(t),∫₀^t k(t,s,x(s))Δs)$,
t ∈ Iₐ = [0,a] ∩ T, a ∈ R₊,
x(0) = x₀
where T denotes a time scale (nonempty closed subset of real numbers R), Iₐ is a time scale interval. Functions f,k are Carathéodory functions with values in a Banach space E and the integral is taken in the sense of Henstock-Kurzweil delta integral, which generalizes the Henstock-Kurzweil integral.
Additionally, functions f and k satisfy some boundary conditions and conditions expressed in terms of measures of noncompactness. Moreover, we prove an Ambrosetti type lemma on a time scale.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2011, 31, 1; 71-90
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Mathematical Modeling of the Competition Between Acquired Immunity and Cancer
Autorzy:
Kolev, M.
Powiązania:
https://bibliotekanauki.pl/articles/908160.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
medycyna
matematyka
leukemia
acquired immunity
immunotherapy
antibodies
integro-differential equations
Opis:
In this paper we propose and analyse a model of the competition between cancer and the acquired immune system. The model is a system of integro-differential bilinear equations. The role of the humoral response is analyzed. The simulations are related to the immunotherapy of tumors with antibodies.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2003, 13, 3; 289-296
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical modelling of the competition between the adaptive immune system and virus
Autorzy:
Kolev, M.
Powiązania:
https://bibliotekanauki.pl/articles/206177.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
numerical modelling
kinetic theory
active particles
integro-differential equations of Boltzmann type
nonlinear dynamics
virus
adaptive immune system
Opis:
We present and analyze numerically a mathematical model of interactions between adaptive immune system and viral infection. The model is a bilinear system of partial integro-differential equations of Boltzmann type. It is a generalization of the recently proposed kinetic models that consider particular (namely, the cellmediated and the humoral) immune mechanisms used in the fight against viral infections. We use Matlab to solve complicated system of equations, present the results of computer simulations and explain their immunological meaning. The results show that the model can describe in a better way (in comparison with the previous kinetic models) real biological situations and is able to illustrate various methods of therapy.
Źródło:
Control and Cybernetics; 2011, 40, 3; 763-778
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical solution of two-dimensional Fredholm integro-differential equations by Chebyshev integral operational matrix method
Autorzy:
Ishola, Christie Yemisi
Taiwo, Omotayo Adebayo
Adebisi, Ajimot Folasade
Peter, Olumuyiwa James
Powiązania:
https://bibliotekanauki.pl/articles/2175510.pdf
Data publikacji:
2022
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Chebyshev polynomials
operational matrix
two-dimensional
Fredholm integro-differential equations
wielomiany Czebyszewa
macierz operacyjna
modele dwuwymiarowe
równanie całkowo-różniczkowe Fredholma
Opis:
This paper presents the Chebyshev Integral Operational Matrix Method (CIOMM) for the numerical solution of two-dimensional Fredholm Integro-Differential Equations (2D-FIDEs). The process of the method is obtaining the operational matrix of integration by evaluating a 2D integral of 2D Chebyshev polynomial basis functions and assuming approximate solutions of the 2D-FIDEs as a truncated 2D Chebyshev series. This leads to a system of linear algebraic equations which are solved to obtain the values of the unknown constants using Maple 18. Some numerical problems are solved to illustrate the practicability of the method.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 1; 29--40
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical study for a second order Fredholm integro-differential equation by applying Galerkin-Chebyshev-wavelets method
Autorzy:
Henka, Youcef
Lemita, Samir
Aissaoui, Mohamed-Zine
Powiązania:
https://bibliotekanauki.pl/articles/2202040.pdf
Data publikacji:
2022
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Fredholm integro-differential equations
nonlinear equation
Galerkin method
Chebyshev wavelets
równanie całkowo-różniczkowe Fredholma
równanie nieliniowe
metoda Galerkina
falki Czebyszewa
Opis:
In the present paper, we apply the Galerkin method using Chebyshev wavelets to approximate the exact solution for a second order Fredholm integro-differential equation with initial conditions. This numerical method gives us a nonlinear algebraic system that would be solved using the Picard successive approximations technique. Furthermore, we show the validity and the ability of the proposed method through some illustrative examples.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 4; 28--39
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 27

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