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Wyświetlanie 1-15 z 123
Tytuł:
On asymptotic expansions of global errors
Autorzy:
Pfeifer, Eckhard
Powiązania:
https://bibliotekanauki.pl/articles/747786.pdf
Data publikacji:
1990
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Finite difference methods
Opis:
.
We consider a linear partial differential equation with constant coefficients and the corresponding difference equation. Conditions are given under which the error possesses an asymptotic expansion with respect to h. These results are applied to obtain asymptotic expansions of some quadratures and of the approximate solution of a boundary value problem for a second order differential equation.
Źródło:
Mathematica Applicanda; 1990, 18, 32
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Explicit Difference Schemes for Nonlinear Differential Functional Parabolic Equations with Mixed Derivatives - Convergence Analysis
Autorzy:
Poliński, Artur
Powiązania:
https://bibliotekanauki.pl/articles/745697.pdf
Data publikacji:
2005
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Finite difference
stability
parabolic
nonlocal
Opis:
We study the initial-value problem for parabolic equations with mixed partial derivatives and constant coefficients, and with nonlinear and nonlocal right-hand sides. Nonlocal terms appear in the unknown function and its gradient. We analyze convergence of explicit finite difference schemes by means of discrete fundamental solutions.
Źródło:
Commentationes Mathematicae; 2005, 45, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
1D and 2D finite-difference operators for periodic functions on arbitrary mesh
Autorzy:
Sobczyk, Tadeusz Jan
Powiązania:
https://bibliotekanauki.pl/articles/2042801.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
arbitrary meshes
finite-difference operators
partial finite difference operators
periodic function
two-variable periodic functions
Opis:
This paper presents novel discrete differential operators for periodic functions of one- and two-variables, which relate the values of the derivatives to the values of the function itself for a set of arbitrarily chosen points over the function’s area. It is very characteristic, that the values of the derivatives at each point depend on the function values at all points in that area. Such operators allow one to easily create finite-difference equations for boundaryvalue problems. The operators are addressed especially to nonlinear differential equations.
Źródło:
Archives of Electrical Engineering; 2022, 71, 1; 265-275
1427-4221
2300-2506
Pojawia się w:
Archives of Electrical Engineering
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Conjugation to a shift and the splitting of invariant manifolds
Autorzy:
Gelfreich, Vassiliĭ
Powiązania:
https://bibliotekanauki.pl/articles/1339264.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
normal form
separatrix splitting
finite-difference equation
Opis:
We give sufficient conditions for a diffeomorphism in the plane to be analytically conjugate to a shift in a complex neighborhood of a segment of an invariant curve. For a family of functions close to the identity uniform estimates are established. As a consequence an exponential upper estimate for splitting of separatrices is established for diffeomorphisms of the plane close to the identity. The constant in the exponent is related to the width of the analyticity domain of the limit flow separatrix. Unlike the previous works the cases of non-area-preserving maps and parabolic fixed points are included.
Źródło:
Applicationes Mathematicae; 1996-1997, 24, 2; 127-140
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The finite difference approximation for the Dirichlet problem with a non-uniform mesh on a boundary
Autorzy:
Morawiec, Grażyna
Powiązania:
https://bibliotekanauki.pl/articles/747719.pdf
Data publikacji:
1987
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Derivation of finite difference approximations
Error bounds
Opis:
.
The author describes a construction of the positive difference scheme, which is the approximation of the Dirichlet problem for an elliptic second order equation with mixed derivatives in an arbitrary region in R2. The a priori estimation for the approximate solution is proved and the estimation of the rate of convergence in maximum norm is established.
Źródło:
Mathematica Applicanda; 1987, 16, 30
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
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:
Finite-difference solution of parabolic equation and numerical simulation for X-ray focusing
Autorzy:
Elsawy, M. H. R. A.
Leble, S.
Powiązania:
https://bibliotekanauki.pl/articles/1954440.pdf
Data publikacji:
2014
Wydawca:
Politechnika Gdańska
Tematy:
finite difference model
focusing X-rays
Runge-Kutta
Opis:
In this paper we apply the finite-difference method to solve a parabolic equation of a general problem of short wave diffraction in a conducting medium. It is based on the implicit Runge-Kutta method of the second order combined with the iterative procedure. We also present new numerical simulations for X-rays focusing using the mentioned approach. We consider CRLs with a parabolic profile with a radius of curvature up to 0.2 mm. The main goal of this work is to elaborate an X-ray calculator for a PC which would present new possibilities compared to conventional ones. The correspondent code is written in FORTRAN to obtain the focal distance and diffraction spot profiles. Simulations for two cases were performed, the first one with 33 Al lenses for X-ray energy 15 keV, the results showed that we needed to consider more than 50000 points in each direction which forced us to consider a one-dimensional simulation only. For the second case we performed a simulation for several lenses, up to 15 Al lenses to perform the 2-d simulation. We have good agreement with the experimental data for the focal distance, and for the intensity at the focal plane while, for the spot size, we have smaller FWHM for the Gaussian beam at the detector than in the experimental data. We believe that the FWHM we have is smaller as our lenses are ideal without any defects.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2014, 18, 1; 101-111
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Parallel and distributed seismic wave-field modeling
Autorzy:
Danek, T.
Franczyk, A.
Powiązania:
https://bibliotekanauki.pl/articles/1964208.pdf
Data publikacji:
2004
Wydawca:
Politechnika Gdańska
Tematy:
wave field modeling
PC clusters
finite difference method
Opis:
Elastic or acoustic wave-field modeling is an important part of seismic exploration. It can be used during the planning, processing and interpretation stages of seismic investigation. First attempts of using wave-field modeling were undertaken in the seventies by Alford, Kelly and others (Alford R M, Kelly K R and Boore D M 1974 Geophysics 39 (6) 834; Kelly K R, Ward R W, Treitel S and Alford R M 1976 Geophysics 41 2). These attempts were restricted by the limitations of computers at that time. Even now, computation for models of the standard exploration scale could last many hours, and many days in case of longer recording times. One of the best methods to overcome this disadvantage is parallelization of computations (Niccanna C and Bean C J 1997 Computers and Geosciences 23 (7) 771; Villareal A and Scales J A 1997 Computers in Physics 11 (4) 388). This paper presents the results of distributed parallelization of elastic and acoustic wave-field modeling based on a Parallel Virtual Machine.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2004, 8, 4; 573-581
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Gold nano-elliptic arrays used in plasmonic waveguides in near infrared spectrum
Autorzy:
Nurmohammadi, T.
Yadipour, R.
Abbasian, K.
Powiązania:
https://bibliotekanauki.pl/articles/174404.pdf
Data publikacji:
2018
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
loss coefficient
group velocity
finite-difference time-domain
Opis:
In this paper, we investigated plasmonic waveguides in near infrared spectrum, especially at original (λ = 1310 nm) and also communication bands (λ = 1550 nm) using gold nano-elliptic rings. It is possible to shift localized surface plasmon resonance, by appropriate geometrical properties, to the desired wavelength. Three-dimensional simulations utilizing the finite-difference time-domain algorithm are used to determine the set of geometrical parameters of gold nano-elliptic rings for exciting localized surface plasmon resonance at 1310 and 1550 nm. Employing different configurations of gold nano-elliptic rings chains, waveguides are designed, with–3 dB transmission loss coefficients and group velocities calculations for different modes. In comparison with circular nanorings, elliptic rings showed better characteristics, such as high electric field enhancements and low loss transmission coefficients.
Źródło:
Optica Applicata; 2018, 48, 3; 489-497
0078-5466
1899-7015
Pojawia się w:
Optica Applicata
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Finite Difference Analysis of Surface Wave Scattering by Underwater Rectangular Obstacles
Autorzy:
Szmidt, K.
Powiązania:
https://bibliotekanauki.pl/articles/241339.pdf
Data publikacji:
2010
Wydawca:
Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
Tematy:
water wave
scattering of waves
finite difference method
Opis:
This paper deals with the problem of the scattering of surface water waves by underwater obstacles. The main goal of the investigations is to estimate the efficiency of such structures in protecting sea shelf zones from open sea waves. A useful measure of the protection is the ratio of the square of the amplitude of the transmitted wave to the square of the amplitude of the arriving wave. The problem is formulated in terms of the finite difference method. It is shown that the discrete approach to the problem leads to eigenvalue problems for two matrices resulting from the discrete description. As compared to analytical formulation, the discrete method may be convenient in application to unsteady problems and obstacles of complicated geometry.
Źródło:
Archives of Hydro-Engineering and Environmental Mechanics; 2010, 57, 3-4; 179-198
1231-3726
Pojawia się w:
Archives of Hydro-Engineering and Environmental Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Loads exerted by floating ice on a cylindrical structure
Autorzy:
Staroszczyk, R.
Powiązania:
https://bibliotekanauki.pl/articles/241206.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Budownictwa Wodnego PAN
Tematy:
floating ice
plate
rheology
creep buckling
finite difference method
Opis:
The paper is concerned with the problem of interaction between a coherent floating ice cover and a fixed, rigid, vertically-walled circular cylinder. The ice cover, of horizontal dimensions considerably larger than the size of the structure, is assumed to be driven against the structure by wind and water current drag stresses. The floating ice cover is modelled as a plate that is subject to the action of horizontal forces and transverse bending due to the reaction of underlying water. During an interaction event, of a quasi-static character, the ice is modelled as a creeping material the behaviour of which is described by a viscous flow law with two, bulk and shear, viscosities. The viscosities change dramatically in their magnitudes during a transition from converging to diverging deformation of the material to reflect the fact that floating ice offers much less resistance to tensile rather than compressive stresses. By numerical simulations carried out by a finite difference method, the influence of the ice rheological parameters on the distribution of contact stresses at the ice - structure interface is investigated. Two types of boundary conditions at the interface, free-slip and no-slip, are considered, and their effects on the loads sustained by the structure are compared. In addition, creep buckling of the ice sheet near the structure is analysed to determine the critical time at which ice starts to fail due to exceeding its flexural strength at given loading conditions.
Źródło:
Archives of Hydro-Engineering and Environmental Mechanics; 2005, 52, 1; 39-58
1231-3726
Pojawia się w:
Archives of Hydro-Engineering and Environmental Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The optimal explicit unconditionally stable box scheme
Autorzy:
Moszyński, Krzysztof
Powiązania:
https://bibliotekanauki.pl/articles/747543.pdf
Data publikacji:
1997
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Finite difference methods
Stability and convergence of numerical methods
Opis:
.
The finite difference “box” scheme, (see also [1],[2]), is considered on the simplest possible model of single first order linear hyperbolic equation: ut+mux=0 with constant, coefficient m, and one space variable. The optimal version of the scheme, which is nonoscilating and unconditionally stable with respect to the initial and boundary conditions, is derived in the class of box schemes of the order at, least one. If apropriately iterated, this ścinane may be applied to general systems of quasilinear first order hyperbolic equations in one space variable, as an explicit, unconditionally stable solver. For more than one space variable this solver is applicable via splitting (see [3]).
Źródło:
Mathematica Applicanda; 1997, 26, 40
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Difference method for a nonlinear parabolic equation of second order in two space variables
Autorzy:
Kawecki, Roman
Powiązania:
https://bibliotekanauki.pl/articles/747916.pdf
Data publikacji:
1990
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Finite difference methods
Stability and convergence of numerical methods
Opis:
.
A.C. Reynolds in his paper (1972) proposed a difference parametric method for solving the Fourier problem for a nonlinear parabolic equation of second order in one space variable. The paper presents a generalization of Reynolds’ method for the problem in two space variables with mixed derivatives. In this paper, Fourier problems for a general class of nonlinear parabolic equation, in QT = Q x [0, T], are studied. To solve this problem we construct a finite difference scheme with a real parameter. We prove that the solutions of certain associated finite difference equations are unique and converge to the solution of the initial-boundary value problem with 0(h^2) rate of convergence.
Źródło:
Mathematica Applicanda; 1990, 18, 32
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dynamic response of three-layered annular plate with imperfections
Autorzy:
Pawlus, D.
Powiązania:
https://bibliotekanauki.pl/articles/178521.pdf
Data publikacji:
2014
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
sandwich
annular plate
dynamic stability
imperfections
finite difference method
finite element method
Opis:
This paper presents the imperfection sensitivity of annular plate with three-layered structure. The plate composed of thin elastic facings and a thicker elastic core is loaded in facing plane. The classical issue of a three-layered plate was solved for dynamic deflection problem using the approximation methods: orthogonalization and finite difference. The solution includes the axisymmetric and asymmetric plate modes of the dynamic stability loss. The evaluation of the rate of plate sensitivity to imperfection of plate preliminary geometry has been enriched by the analysis of plate models built of finite elements. The ABAQUS program has been used. The numerous calculation results in the form of deflection characteristics, buckling modes, values of critical parameters create the view of response of dynamic plate structure with different rate of imperfection and linear in time loading growth, too.
Źródło:
Studia Geotechnica et Mechanica; 2014, 36, 4; 13-25
0137-6365
2083-831X
Pojawia się w:
Studia Geotechnica et Mechanica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Modelling and analysis of fibre microlenses with ray-tracing and finite-difference methods
Autorzy:
Śliwak, Adam
Jeleń, Mateusz
Patela, Sergiusz
Powiązania:
https://bibliotekanauki.pl/articles/2063899.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Stowarzyszenie Elektryków Polskich
Tematy:
Finite-difference time-domain method
knife-edge method
microlens
raytracing
Opis:
Fibre optic microlenses are small optical elements formed on the end-faces of optical fibres. Their dimensions range from a few tens to hundreds of micrometres. In the article, four optical fibre microlenses are modelled and analysed. Microlenses are used for light beam manipulation and quantitative metrics are needed to evaluate the results, for example, the size of focusing spot or intensity distribution. All four lenses tested are made of rods of the same refractive index; they were welded to a single-mode fibre. Two modelling methods were used to analyse the lenses: ray-tracing and finite-difference time-domain. The ray-tracing algorithm moves rays from one plane to another and refracts them on the surfaces. Finite-difference time-domain consists of calculating Maxwell’s equations by replacing spatial and temporal derivatives by quotients of finite differences. In this paper, the results of the microlenses analyses obtained from ray-tracing and finite-difference timedomain methods were compared. Both mets of analysis showed the presence of undesirable side lobes related to lens design, namely rods too long for lens fabrication. The test results were compared with the measurements made with the knife-edge method. The use of a single tool to determine parameters of an optical fibre lens does not allow for precise determination of its properties. It is necessary to use different tools and programs. This allows a complete analysis of the beam parameters, letting us find the causes of technical issues that limit the performance of the lenses.
Źródło:
Opto-Electronics Review; 2022, 30, 1; 1--9
1230-3402
Pojawia się w:
Opto-Electronics Review
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 123

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