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Wyświetlanie 1-15 z 19
Tytuł:
Convergence results for unbounded solutions of first order non-linear differential-functional equations
Autorzy:
Leszczyński, Henryk
Powiązania:
https://bibliotekanauki.pl/articles/1311094.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
error estimates
recurrence inequalities
difference scheme
Opis:
We consider the Cauchy problem in an unbounded region for equations of the type either $D_{t}z(t,x) = f(t,x,z(t,x),z_{(t,x)},D_{x}z(t,x))$ or $D_{t}z(t,x)= f(t,x,z(t,x),z,D_{x}z(t,x))$. We prove convergence of their difference analogues by means of recurrence inequalities in some wide classes of unbounded functions.
Źródło:
Annales Polonici Mathematici; 1996, 64, 1; 1-16
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
OVERLAPPING MULTIGRID METHODS AS AN EFFICIENT APPROACH FOR SOLVING THE BLACK-SCHOLES EQUATION
Autorzy:
Bernardelli, Michał
Powiązania:
https://bibliotekanauki.pl/articles/453023.pdf
Data publikacji:
2015
Wydawca:
Szkoła Główna Gospodarstwa Wiejskiego w Warszawie. Katedra Ekonometrii i Statystyki
Tematy:
option pricing
Black-Scholes model
multigrid method
finite-difference scheme
Opis:
In this paper the modification of a two-level multigrid method by allowing an overlap between adjacent subdomains and its application to a one-dimensional Black-Scholes equation is described. The method is based on the finite-difference schema known as implicit Euler. Numerical experiments confirm the superiority of the proposed method in relation to the classic multigrid method in form of shortening computation time, memory savings and ease of parallelization. The comparison shows the advantages of overlapping grids vs method without them, mainly due to improved accuracy of the solution.
Źródło:
Metody Ilościowe w Badaniach Ekonomicznych; 2015, 16, 1; 25-36
2082-792X
Pojawia się w:
Metody Ilościowe w Badaniach Ekonomicznych
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Explicit Finite-Difference Scheme for the Numerical Solution of the Model Equation of Nonlinear Hereditary Oscillator with Variable-Order Fractional Derivatives
Autorzy:
Parovik, R. I.
Powiązania:
https://bibliotekanauki.pl/articles/229615.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
nonlinear hereditary oscillator
finite difference scheme
Cauchy problem
fractional derivatives
numerical experiment
Opis:
The paper deals with the model of variable-order nonlinear hereditary oscillator based on a numerical finite-difference scheme. Numerical experiments have been carried out to evaluate the stability and convergence of the difference scheme. It is argued that the approximation, stability and convergence are of the first order, while the scheme is stable and converges to the exact solution
Źródło:
Archives of Control Sciences; 2016, 26, 3; 429-435
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Investigation of the Stability and Convergence of Difference Schemes for the Three-dimensional Equations of the Atmospheric Boundary Layer
Autorzy:
Temirbekov, A. N.
Urmashev, B. A.
Gromaszek, K.
Powiązania:
https://bibliotekanauki.pl/articles/226826.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
atmospheric boundary layer equations
difference scheme
approximation error
stability
convergence algorithms
numerical solution
Opis:
In this article we construct a finite-difference scheme for the three-dimensional equations of the atmospheric boundary layer. The solvability of the mathematical model is proved and quality properties of the solutions are studied. A priori estimates are derived for the solution of the differential equations. The mathematical questions of the difference schemes for the equations of the atmospheric boundary layer are studied. Nonlinear terms are approximated such that the integral term of the identity vanishes when it is scalar multiplied. This property of the difference scheme is formulated as a lemma. Main a priori estimates for the solution of the difference problem are derived. Approximation properties are investigated and the theorem of convergence of the difference solution to the solution of the differential problem is proved.
Źródło:
International Journal of Electronics and Telecommunications; 2018, 64, 3; 391-396
2300-1933
Pojawia się w:
International Journal of Electronics and Telecommunications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A numerical solution for a class of time fractional diffusion equations with delay
Autorzy:
Pimenov, V. G.
Hendy, A. S.
Powiązania:
https://bibliotekanauki.pl/articles/330624.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
fractional diffusion equation
difference scheme
convergence analysis
równanie dyfuzji ułamkowe
schemat różnicowy
analiza zbieżności
Opis:
This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ 2−α + h4) in L ∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2017, 27, 3; 477-488
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A finite difference method for nonlinear parabolic-elliptic systems of second-order partial differential equations
Autorzy:
Malec, M.
Sapa, L.
Powiązania:
https://bibliotekanauki.pl/articles/255499.pdf
Data publikacji:
2007
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
partial differential equation
parabolic-elliptic system
finite difference method
finite difference scheme
consistence
convergence
stability
error estimate
uniqueness
Opis:
This paper deals with a finite difference method for a wide class of weakly coupled nonlinear second-order partial differential systems with initial condition and weakly coupled nonlinear implicit boundary conditions. One part of each system is of the parabolic type (degenerated parabolic equations) and the other of the elliptic type (equations with a parameter) in a cube in R1+n. A suitable finite difference scheme is constructed. It is proved that the scheme has a unique solution, and the numerical method is consistent, convergent and stable. The error estimate is given. Moreover, by the method, the differential problem has at most one classical solution. The proof is based on the Banach fixed-point theorem, the maximum principle for difference functional systems of the parabolic type and some new difference inequalities. It is a new technique of studying the mixed-type systems. Examples of physical applications and numerical experiments are presented.
Źródło:
Opuscula Mathematica; 2007, 27, 2; 259-289
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Implicit solution of 1d nonlinear porous medium equation using the four-point Newton- EGMSOR iterative method
Autorzy:
Chew, J. V. L.
Sulaiman, J.
Powiązania:
https://bibliotekanauki.pl/articles/122819.pdf
Data publikacji:
2016
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
porous medium equation
finite difference scheme
Newton method
Explicit Group
MSOR
równania różniczkowe cząstkowe
metoda różnic skończonych
metoda Newtona
Opis:
The numerical method can be a good choice in solving nonlinear partial differential equations (PDEs) due to the difficulty in finding the analytical solution. Porous medium equation (PME) is one of the nonlinear PDEs which exists in many realistic problems. This paper proposes a four-point Newton-EGMSOR (4-Newton-EGMSOR) iterative method in solving 1D nonlinear PMEs. The reliability of the 4-Newton-EGMSOR iterative method in computing approximate solutions for several selected PME problems is shown with comparison to 4-Newton-EGSOR, 4-Newton-EG and Newton-Gauss-Seidel methods. Numerical results showed that the proposed method is superior in terms of the number of iterations and computational time compared to the other three tested iterative methods.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 2; 11-21
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Finite difference method for the fractional order pseudo telegraph integro-differential equation
Autorzy:
Modanli, Mahmut
Ozbag, Fatih
Akgül, Ali
Powiązania:
https://bibliotekanauki.pl/articles/2175509.pdf
Data publikacji:
2022
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
pseudo telegraph equation
integro-differential equation
finite difference scheme
stability analysis
równanie całkowo-różniczkowe
metoda różnic skończonych
analiza stabilności
Opis:
The main goal of this paper is to investigate the numerical solution of the fractional order pseudo telegraph integro-differential equation. We establish the first order finite difference scheme. Then for the stability analysis of the constructed difference scheme, we give theoretical statements and prove them. We also support our theoretical statements by performing numerical experiments for some fractions of order α.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 1; 41--54
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
MHD free convection-radiation interaction in a porous medium - part I: numerical investigation
Autorzy:
Vasu, B.
Gorla, R. S. R.
Murthy, P. V. S. N.
Prasad, V. R.
Bég, O. Anwar
Siddiqa, S.
Powiązania:
https://bibliotekanauki.pl/articles/266199.pdf
Data publikacji:
2020
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
pole magnetyczne
metoda Keller-Box
nośnik porowaty
implicit finite difference scheme
Keller-Box method
magnetic field
horizontal circular cylinder
Opis:
A numerical investigation of two dimensional steady magnetohydrodynamics heat and mass transfer by laminar free convection from a radiative horizontal circular cylinder in a non-Darcy porous medium is presented by taking into account the Soret/Dufour effects. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller–Box finite-difference scheme. We use simple central difference derivatives and averages at the mid points of net rectangles to get finite difference equations with a second order truncation error. We have conducted a grid sensitivity and time calculation of the solution execution. Numerical results are obtained for the velocity, temperature and concentration distributions, as well as the local skin friction, Nusselt number and Sherwood number for several values of the parameters. The dependency of the thermophysical properties has been discussed on the parameters and shown graphically. The Darcy number accelerates the flow due to a corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance. A comparative study between the previously published and present results in a limiting sense is found in an excellent agreement.
Źródło:
International Journal of Applied Mechanics and Engineering; 2020, 25, 1; 198-218
1734-4492
2353-9003
Pojawia się w:
International Journal of Applied Mechanics and Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Modelling of heat and flow phenomena occuring in waterwall tubes of boilers for supercritical steam parameters
Autorzy:
Zima, W.
Grądziel, S.
Cebula, A.
Powiązania:
https://bibliotekanauki.pl/articles/240331.pdf
Data publikacji:
2010
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
ekran wodny
model matematyczny
parametry nadkrytyczne
parametry rozłożone
schemat różnicowy
distributed parameters
Implicit difference scheme
mathematical model
supercritical parameters
waterwalls
Opis:
In this paper a mathematical model enabling the analysis of the heat-flow phenomena occurring in the waterwalls of the combustion chambers of the boilers for supercritical parameters is proposed. It is a one-dimensional model with distributed parameters based on the solution of equations describing the conservation laws of mass, momentum, and energy. The purpose of the numerical calculations is to determine the distributions of the fluid enthalpy and the temperature of the waterwall pipes. This temperature should not exceed the calculation temperature for particular category of steel. The derived differential equations are solved using two methods: with the use of the implicit difference scheme, in which the mesh with regular nodes was applied, and using the Runge-Kutta method. The temperature distribution of the waterwall pipes is determined using the CFD. All thermophysical properties of the fluid and waterwall pipes are computed in real-time. The time-spatial heat transfer coefficient distribution is also computed in the on-line mode. The heat calculations for the combustion chamber are carried out with the use of the zone method, thus the thermal load distribution of the waterwalls is known. The time needed for the computations is of great importance when taking into consideration calculations carried out in the on-line mode. A correctly solved one-dimensional model ensures the appropriately short computational time.
Źródło:
Archives of Thermodynamics; 2010, 31, 3; 19-31
1231-0956
2083-6023
Pojawia się w:
Archives of Thermodynamics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Numerical solution for the problem of heat and mass flow in the soil heated with warm air
Autorzy:
Bożek, B.
Kurpaska, S.
Powiązania:
https://bibliotekanauki.pl/articles/241006.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
Tematy:
numerical solution
heat flow
mass flow
soils
warm air
differential equations
greenhouse substrate
system of heating pipes
explicite-implicite difference scheme
Opis:
In this paper a difference method of solving the system of differential equations is presented for differential equations, describing the distribution of temperature and water content in the greenhouse substrate heated with a system of heating pipes. The algorithm of solving the proposed method (explicite-implicite difference scheme) is presented. In addition, the effects of temperature and water content changes obtained from the solution of proposed the model as well as the model where the thermal diffusion of mass was included were compared.
Źródło:
Archives of Hydro-Engineering and Environmental Mechanics; 2000, 47, 1-4; 75-96
1231-3726
Pojawia się w:
Archives of Hydro-Engineering and Environmental Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Third order singularly perturbed delay differential equation of reaction diffusion type with integral boundary condition
Autorzy:
Sekar, Elango
Tamilselvan, Ayyadurai
Powiązania:
https://bibliotekanauki.pl/articles/122568.pdf
Data publikacji:
2019
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
singular perturbation problem
finite difference scheme
delay
integral boundary condition
error estimate
schemat różnic skończonych
opóźnienie
oszacowanie błędu
metoda numeryczna
metoda równań skończonych
Opis:
A class of third order singularly perturbed delay differential equations of reaction diffusion type with an integral boundary condition is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The method suggested is of almost first order convergent. An error estimate is derived in the discrete norm. Numerical examples are presented, which validate the theoretical estimates.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 2; 99-110
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Implicit scheme of the finite difference method for the second-order dual phase lag equation
Autorzy:
Majchrzak, E.
Mochnacki, B.
Powiązania:
https://bibliotekanauki.pl/articles/280549.pdf
Data publikacji:
2018
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
microscale heat transfer
dual phase lag model
implicit scheme of finite difference method
Opis:
The second-order dual phase lag equation (DPLE) as a mathematical model of the microscale heat transfer is considered. It is known that the starting point determining the final form of this equation is the generalized Fourier law in which two positive constants (the relaxation and thermalization times) appear. Depending on the order of the generalized Fourier law expansion into the Taylor series, different forms of the DPLE can be obtained. As an example of the problem described by the second-order DPLE equation, thermal processes proceeding in the domain of a thin metal film subjected to a laser pulse are considered. The numerical algorithm is based on an implicit scheme of the finite difference method. At the stage of numerical modeling, the first, second and mixed order of the dual phase lag equation are considered. In the final part of the paper, examples of different solutions are presented and conclusions are formulated.
Źródło:
Journal of Theoretical and Applied Mechanics; 2018, 56, 2; 393-402
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dual-phase lag equation. Stability conditions of a numerical algorithm based on the explicit scheme of the finite difference method
Autorzy:
Majchrzak, E.
Mochnacki, B.
Powiązania:
https://bibliotekanauki.pl/articles/122742.pdf
Data publikacji:
2016
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
heat conduction
dual-phase lag equation
finite difference method
stability conditions of FDM explicit scheme
przewodzenie ciepła
metoda różnic skończonych
Opis:
The dual-phase lag equation (DPLE) is considered. This equation belongs to the group of hyperbolic PDE, contains a second order time derivative and higher order mixed derivative in both time and space. From the engineer’s point of view, the DPLE results from the generalized form of the Fourier law. It is applied as a mathematical model of thermal processes proceeding in the micro-scale and also in the case of bio-heat transfer problem analysis. At the stage of numerical computations the different approximate methods of the PDE solving can be used. In this paper, the authors present the considerations concerning the stability conditions of the explicit scheme of finite difference method (FDM). The appropriate conditions have been found using the von Neumann analysis. In the final part of the paper, the results of testing computations are shown.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 3; 89-96
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Cattaneo-Vernotte bioheat transfer equation. Stability conditions of numerical algorithm based on the explicit scheme of the finite difference method
Autorzy:
Mochnacki, B.
Tuzikiewicz, W.
Powiązania:
https://bibliotekanauki.pl/articles/122475.pdf
Data publikacji:
2016
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
bioheat transfer
Cattaneo-Vernotte equation
finite difference method
stability conditions of FDM explicit scheme
przepływ biociepła
równanie Cattaneo-Vernotte
metoda różnic skończonych
Opis:
The Cattaneo-Vernotte (CVE) equation is considered. This equation belongs to the group of hyperbolic PDE. Supplementing this equation by two additional terms corresponding to perfusion and metabolic heat sources one can apply the CVE as a mathematical model describing the heat transfer processes proceeding in domain of the soft tissue. Such an approach is recently often preferred substituting the classical Pennes model. At the stage of numerical computations the different numerical methods of the PDE solving can be used. In this paper the problems of stability conditions for the explicit scheme of the finite difference method (FDM) are discussed. The appropriate condition limiting the admissible time step have been found using the von Neumann analysis.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 4; 137-144
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 19

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