Wyniki wyszukiwania - Biblioteka Nauki

1

Thermal performance of porous fins with temperature-dependent heat generation via the homotopy perturbation method and collocation method

100%

Hoshyar H. A. , Rahimipetroudi I. , Ganji D. D. , Majidian A. R.

Journal of Applied Mathematics and Computational Mechanics

|

2015

|

tom Vol. 14, nr 4

53--65

EN

An analysis has been performed to study the problem of the thermal performance of a nonlinear problem of the porous fin with temperature-dependent internal heat generation. Highly accurate semi-analytical methods called the collocation method (CM) and the homotopy perturbation method (HPM) are introduced and then are used to obtain a nonlinear temperature distribution equation in a longitudinal porous fin. This study is performed using passage velocity from the Darcy’s model to formulate the heat transfer equation through porous media. The heat generation is assumed to be a function of temperature. The effects of the natural convection parameter Nc, internal heat generation εg, porosity Sh and generation number G parameter on the dimensionless temperature distribution are discussed. Also, numerical calculations called the fourth order Runge-Kutta method were carried out for the various parameters entering into the problem for validation. Results reveal that analytical approaches are very effective and convenient. Also it is found that these methods can achieve more suitable results compared to numerical methods.

2

The Use of the Collocation Method for Solving the Diffusion Equation under Two Mass Specifications

100%

Derkach S.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

|

2003

|

tom Vol. 9

31--33

EN

In this paper the diffusion equation [formula] with the initial condition [formula] is considered.

3

Collocation method for the Sturm-Liouville eigenvalue problem

100%

Grabarski A.

Demonstratio Mathematica

|

1998

|

tom Vol. 31, nr 1

111-119

4

Flow past a sphere moving towards a wall in micropolar fluid

100%

Kucaba-Piętal A.

Journal of Theoretical and Applied Mechanics

|

1999

|

tom nr 2

301-318

EN

The paper presents the first "exact" solution to the problem of creeping flow past a sphere mowing towards a wall in micropolar fluid. The analytical-numerical method is presented, that is a development of the boundary collocation technique previously used for solving many corresponding problems for a Newtonian fluid. The initial study of the method has been carried out and the results for a force acting on a sphere compared with their counterparts for a Newtonial fluid are presented. It is worth while to note that the drag force on a sphere depends on material constants of the micropolea fluid and the distance from the wall.

PL

Rozwiązane zostało zagadnienie wyznaczenia pola przepływu i działającej siły na cząstkę kulistą poruszającą się w kierunki ścianki w płynie mikropolarnym. Skonstruowano metodę analityczno-- --numeryczną w oparciu o metodę kolokacji. Rozpatrzono przepływ quasistacjonarny w przybliżeniu Stokesa.

5

Numerical solution of fractional differential equations by using fractional B-spline

100%

Jafari H. , Khalique C. , Ramezani M. , Tajadodi H.

Open Physics

|

2013

|

tom 11

|

nr 10

1372-1376

EN

In this paper, we present fractional B-spline collocation method for the numerical solution of fractional differential equations. We consider this method for solving linear fractional differential equations which involve Caputo-type fractional derivatives. The numerical results demonstrate that the method is efficient and quite accurate and it requires relatively less computational work. For this reason one can conclude that this method has advantage on other methods and hence demonstrates the importance of this work.

6

A Numerical Approach of the sentinel method for distributed parameter systems

100%

Traore A. , Mampassi B. , Saley B.

Open Mathematics

|

2007

|

tom 5

|

nr 4

751-763

EN

In this paper we consider the problem of detecting pollution in some non linear parabolic systems using the sentinel method. For this purpose we develop and analyze a new approach to the discretization which pays careful attention to the stability of the solution. To illustrate convergence properties we give some numerical results that present good properties and show new ways for building discrete sentinels.

7

Accurate numerical approximation of nonlinear fourth order Emden-Fowler type equations: A Haar based wavelet-collocation approach

100%

Khan N. A. , Shaikh A. , Ayaz M.

Waves, Wavelets and Fractals

|

2017

|

tom 3

|

nr 1

75-83

EN

The motivation of this paper is to study the fourth order Emden-Fowler equations with initial values by Haarwavelet collocation method(HWCM). In this methodology, differential equations are transformed into a system of linear or nonlinear equations that leads to the value of Haar coefficients and later the solution can be obtained on the entire domain (0, 1]. The fourth order nonlinear test examples are solved at different Haar levels to analyze the accuracy of results. The simplicity and effectiveness of the method made it more attractive than non-perturbative methods found in literature.

8

A shifted Jacobi collocation algorithm for wave type equations with non-local conservation conditions

88%

Doha E. , Bhrawy A. , Abdelkawy M.

Open Physics

|

2014

|

tom 12

|

nr 9

637-653

EN

In this paper, we propose an efficient spectral collocation algorithm to solve numerically wave type equations subject to initial, boundary and non-local conservation conditions. The shifted Jacobi pseudospectral approximation is investigated for the discretization of the spatial variable of such equations. It possesses spectral accuracy in the spatial variable. The shifted Jacobi-Gauss-Lobatto (SJ-GL) quadrature rule is established for treating the non-local conservation conditions, and then the problem with its initial and non-local boundary conditions are reduced to a system of second-order ordinary differential equations in temporal variable. This system is solved by two-stage forth-order A-stable implicit RK scheme. Five numerical examples with comparisons are given. The computational results demonstrate that the proposed algorithm is more accurate than finite difference method, method of lines and spline collocation approach

9

Numerical solutions of the reaction diffusion system by using exponential cubic B-spline collocation algorithms

88%

Ersoy O. , Dag I.

Open Physics

|

2015

|

tom 13

|

nr 1

EN

The solutions of the reaction-diffusion system are given by method of collocation based on the exponential B-splines. Thus the reaction-diffusion systemturns into an iterative banded algebraic matrix equation. Solution of the matrix equation is carried out byway of Thomas algorithm. The present methods test on both linear and nonlinear problems. The results are documented to compare with some earlier studies by use of L∞ and relative error norm for problems respectively.

10

Comparison of determination methods of vibration's damping coefficients for complex structures

88%

Flaga A. , Szulej J. , Wielgos P.

Budownictwo i Architektura

|

2008

|

tom vol. 3, nr 2

53-61

EN

The purpose of this paper is to present methods of vibrations damping coefficient determination. The methods, such as collocation method, two energetic methods and half-power bandwidth method concern composite structures. The verification of methods has been taken into account in this work. Two real compound models and two numerical models have been created. Time series of vibrations of these models have been measured and calculated. The comparison of four methods has been made on the basis of obtained results.

11

Multi-frontal parallel direct solver for one dimensional isogeometric collocation method

88%

Lipski P. , Paszyński M.

Computer Methods in Materials Science

|

2015

|

tom Vol. 15, No.1

192--197

EN

In this paper wc present a new multi-frontal solver for the isogeometric collocation method (ISO-C) on GPU. The ISO-C method constitutes an alternative for the isogeometric finite element method (ISO-FEM). The key advantage of ISO-C over ISO-FEM is that it does not include the computationally intensive operation of integrating the variational formulation. The ISO-C method requires using only a single collocation point per one basis function, whereas in ISO-FEM, Gaussian quadrature is applied on many points at each finite element. The presented multi-frontal solver for collocation method results in logarithmic execution time assuming that large enough number of GPU processors is available. In this article, the method is employed for an exemplary ID nanolithography problem of Step-and-Flash Imprint Lithography (SFIL). The algorithm, however, may be applied to a wide class of 2D and 3D problems.

PL

W artykule przedstawiamy nowy solwer wielofrontalny dla izogeometrycznej metody kolokacji (ISO-C) na GPU. Metoda ISO-C stanowi alternatywę dla izogeometrycznej metody elementów skończonych (ISO-FEM). Główną zaletą metody ISO-C jest redukcja znacznego kosztu obliczeniowego całkowania sformułowania wariacyjnego występującego w metodzie ISO-FEM. Metoda ISO-C wymaga bowiem użycia tylko jednego punktu kolokacji dla jednej funkcji bazowej, podczas gdy metoda ISO-FEM wiąże się z zastosowaniem kwadratury Gaussa w wielu punktach na każdym elemencie skończonym. Prezentowany solwer wielofrontalny dla metody kolokacji uzyskuje logarytmiczną złożoność obliczeniową przy założeniu odpowiednio dużej liczby procesorów graficznych GPU. Niniejsza publikacja przedstawia proste wykorzystanie metody dla jednowymiarowego przykładowego problemu nanolitografii Step-and-Flash Imprint Lithography (SFIL). Zaprezentowany algorytm znajduje jednak ogólnie zastosowanie dla szerokiej klasy problemów w dwóch i trzech wymiarach.

12

Legendre multiwavelet collocation method for solving the linear fractional time delay systems

88%

Yousefi S. , Lotfi A.

Open Physics

|

2013

|

tom 11

|

nr 10

1463-1469

EN

In this article the Legendre multiwavelet basis with aid of collocation method has been applied to give approximate solution for fractional delay systems. The properties of Legendre multiwavelet are presented. These properties together with the collocation method are then utilized to reduce the problem to the solution of algebraic system. Numerical results and comparison with exact solutions in the cases when we have exact solution are given in test examples in order to demonstrate the applicability and efficiency of the method.

13

Bernstein operational matrix of differentiation and collocation approach for a class of three-point singular BVPs: error estimate and convergence analysis

88%

Sriwastav N. , Barnwal A. K. , Wazwaz A.-M. , Singh M.

Opuscula Mathematica

|

2023

|

tom Vol. 43, no. 4

575--601

EN

Singular boundary value problems (BVPs) have widespread applications in the field of engineering, chemical science, astrophysics and mathematical biology. Finding an approximate solution to a problem with both singularity and non-linearity is highly challenging. The goal of the current study is to establish a numerical approach for dealing with problems involving three-point boundary conditions. The Bernstein polynomials and collocation nodes of a domain are used for developing the proposed numerical approach. The straightforward mathematical formulation and easy to code, makes the proposed numerical method accessible and adaptable for the researchers working in the field of engineering and sciences. The priori error estimate and convergence analysis are carried out to affirm the viability of the proposed method. Various examples are considered and worked out in order to illustrate its applicability and effectiveness. The results demonstrate excellent accuracy and efficiency compared to the other existing methods.

14

Collocation method based on barycentric interpolation iteration for analysis of nonlinear microbeams

88%

Zhuang M. , Miao C. , Wang Z.

Journal of Theoretical and Applied Mechanics

|

2018

|

tom Vol. 56 nr 3

741--749

EN

A powerful computational methodology, named the barycentric Lagrange interpolation iteration collocation method (BLIICM), for solving nonlinear bending problems of a doubly clamped microbeam under electrostatic loads is presented. The nonlinear governing equation of the microbeam is converted into a linear diﬀerential equation by assuming the initial function. The barycentric Lagrange interpolation collocation method (BLICM) is used to solve the linear diﬀerential equation. The direct linearization formulations and Newton linearization calculation formulations for the nonlinear diﬀerential equation have been given. The calculation method and formulation of the nonlinear integral term have been discussed in details. By applying a barycentric Lagrange interpolation diﬀerential matrix, a matrix-vector calculation formula of BLIICM has been established. Numerical results of calculation examples show that the advantages of the proposed methodology are eﬃcient, simple and of high precision.

15

Problemy wyznaczania współczynnika tłumienia metodą kolokacyjną

88%

Szulej J.

Zeszyty Naukowe. Budownictwo / Politechnika Śląska

|

2006

|

tom z. 109

379-386

PL

W artykule przedstawiono problemy związane z zastosowaniem metody kolokacyjnej. Wymieniona metoda służy do określania współczynnika tłumienia drgającej konstrukcji. Wartość współczynnika tłumienia drgań otrzymujemy na podstawie analizy widmowej przebiegów czasowych przyspieszeń badanych konstrukcji. Wykresy funkcji FFT są porównywane z odpowiednią funkcją aproksymującą. Wynikiem porównania jest między innymi współczynnik tłumienia, który jest jednym z parametrów funkcji aproksymującej. Celem pośrednim jest wyznaczenie poziomu tłumienia materiałowego dla prostych i zespolonych modeli materiałowych.

EN

The problem of practical application of the collocation method have been presented in the paper. This method is used to determine a damping coefficient for a vibrating structure. Its value is obtained by spectral analysis for time series of acceleration. The graphs of FFT functions are compared with suitable approximating functions. The effect of this comparison is the damping coefficient which is one of parameters of the approximating function. Additionaly the level of structural damping for simple and comlex models are found.

16

New Numerical Approach for Solving Abel’s Integral Equations

88%

Anapalı Şenel A. , Öztürk Y. , Gülsu M.

Foundations of Computing and Decision Sciences

|

2021

|

tom Vol. 46, No. 3

255--271

EN

In this article, we present an efficient method for solving Abel’s integral equations. This important equation is consisting of an integral equation that is modeling many problems in literature. Our proposed method is based on first taking the truncated Taylor expansions of the solution function and fractional derivatives, then substituting their matrix forms into the equation. The main character behind this technique’s approach is that it reduces such problems to solving a system of algebraic equations, thus greatly simplifying the problem. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method. Figures and tables are demonstrated to solutions impress. Also, all numerical examples are solved with the aid of Maple.

17

A new geoid for Brunei Darussalam by the collocation method

88%

Lyszkowicz A. , Biryło M. , Becek K.

|

nr 2

18

Capacitance calculation for conductive path : screen layer system in hybrid circuit

75%

Wisz B.

Elektronika : konstrukcje, technologie, zastosowania

|

2007

|

tom Vol. 48, nr 12

43-46

EN

The some calculation ways of capacitance values between conductive path located on the surface of dielectric substrate together with metallic screen on its opposite side are presented in this paper. The submitted method is based on the solution of two-dimensional boundary problem. Electrical potential is presented here in the form of Fourier integrals, fulfilling the Laplace's equation. As the resul- after mathematical transformation -the integral equation for the distribution of electrical charges is obtained, which is next solved by application of numerical method. On this basis the capacitance value has been calculated and experimentally verified.

PL

Zaprezentowano sposoby obliczania wartości pojemności pomiędzy umieszczoną na jednej stronie dielektrycznego podłoża ścieżką przewodzącą a płaszczyzną masy po jego drugiej stronie. Zastosowana metoda polega na rozwiązaniu dwuwymiarowego zagadnienia brzegowego. Potencjał elektryczny przedstawiony w postaci całek Fouriera spełnia równanie Laplace'a. Po matematycznych przekształceniach otrzymuje się w rezultacie równanie całkowe dla rozkładu gęstości ładunku elektrycznego, które jest następnie rozwiązywane metodą numeryczną. Na tej podstawie obliczono wartość pojemności i przeprowadzono jej doświadczalną weryfikację.

19

Application of Chebyshev Collocation Method to Solving the Heat Equation

75%

Povstenko J.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

|

2000/2001

|

tom Vol. 8

57--66

20

A new geoid for Brunei Darussalam by the collocation method

75%

Lyszkowicz A. , Birylo M. , Becek K.

Geodesy and Cartography

|

2014

|

tom Vol. 63, no. 2

183--198

EN

Computation of a new gravimetric geoid in Brunei was carried out Rusing terrestrial, airborne and altimetric gravity data and the EGM08 geopotential model by the collocation method. The computations were carried out by the „remove-restore” technique. In order to have better insight in the quality of input data the estimation of accuracy of the gravity data and geoid undulations from GPS/levelling data was carried out using EGM08 geopotential model. It shows a poor quality of GPS/levelling data. Result of the computation is the gravimetric geoid for the territory of Brunei computed by collocation method with an accuracy estimated below of ±0.3 m.

PL

Wyznaczenie przebiegu nowej geoidy na obszarze Brunei zostało zrealizowane z wykorzystaniem lądowych, lotniczych i altimetrycznych danych grawimetrycznych oraz modelu geopotencjału EGM08 metodą kolokacji. Obliczenia zostały przeprowadzone z wykorzystaniem techniki „removerestore”. W celu uzyskania lepszego wglądu, w jakość danych wejściowych oszacowano dokładność danych grawimetrycznych i geometrycznych odstępów geoidy od elipsoidy na punkach sieci GPS wykorzystując do tego celu model geopotencjału EGM08. Z przyprowadzonych oszacowań wynika przede wszystkim niska dokładność danych GPS/niwelacja. Wynikiem przeprowadzonych obliczeń jest grawimetryczna geoida dla obszaru Brunei, obliczona metodą kolokacji, której dokładność szacuje się poniżej ±0.3 m.