Journal articles: 'Thomas equation'

1

Sakovich, S. Y. "On the Thomas equation." Journal of Physics A: Mathematical and General 21, no. 23 (1988): L1123—L1126. http://dx.doi.org/10.1088/0305-4470/21/23/003.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Al-Ghafri, K. S. "On the Exact Solutions of the Thomas Equation by Algebraic Methods." International Journal of Nonlinear Sciences and Numerical Simulation 16, no. 2 (2015): 73–77. http://dx.doi.org/10.1515/ijnsns-2014-0049.

Full text

Abstract:

AbstractThe Thomas equation is studied to obtain new exact solutions. The wave transformation technique is applied to simplify the main form of the Thomas equation from partial differential equation (PDE) to an ordinary differential equation (ODE). The modified tanh and ($$G'/G$$)-expansion methods are used with the aid of Maple software to arrive at exact solutions for the Thomas equation. Many types of solutions are obtained.

APA, Harvard, Vancouver, ISO, and other styles

3

Bluman, G. W., and S. Kumei. "Symmetry-based algorithms to relate partial differential equations: II. Linearization by nonlocal symmetries." European Journal of Applied Mathematics 1, no. 3 (1990): 217–23. http://dx.doi.org/10.1017/s0956792500000188.

Full text

Abstract:

An algorithm is presented to linearize nonlinear partial differential equations by non-invertible mappings. The algorithm depends on finding nonlocal symmetries of the given equations which are realized as appropriate local symmetries of a related auxiliary system. Examples include the Hopf-Cole transformation and the linearizations of a nonlinear heat conduction equation, a nonlinear telegraph equation, and the Thomas equations.

APA, Harvard, Vancouver, ISO, and other styles

4

Tafrikan, Mohammad, and Mohammad Ghani. "Iterative Method of Thomas Algorithm on The Case Study of Energy Equation." Postulat : Jurnal Inovasi Pendidikan Matematika 3, no. 1 (2022): 14. http://dx.doi.org/10.30587/postulat.v3i1.4346.

Full text

Abstract:

Implicit method is one of the finite difference method and is widely used for discretization some of ordinary or partial differential equations, such like: advection equation, heat transfer equation, burger equation, and many others. Implicit method is unconditionally stable and has been proved with the approximation of Von-Neumann stability criterion. Actually, implicit method is always identical to block matrices (tri-diagonal matrices or penta-diagonal matrices). These matrices can be solved numerically by Thomas algorithm including Gauss elimination using pivot or not, backward or forward substitution. Furthermore, it can be also solved using LU decomposition method with the elimination of lower triangle matrices first and then the elimination of upper triangle matrices. In this research, Thomas algorithm is used to solve numerically for the problem of convective flow on boundary layer, especially for energy equation with the variation of Prandtl number ( ).

APA, Harvard, Vancouver, ISO, and other styles

5

El-Nahhas, A. "Analytic Approximations for Thomas-Fermi Equation." Acta Physica Polonica A 114, no. 4 (2008): 913–18. http://dx.doi.org/10.12693/aphyspola.114.913.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Ashbaugh, Mark S., Rafael D. Benguria, and Cecilia Yarur. "Thomas-Fermi-von Weizs�cker equation." Duke Mathematical Journal 63, no. 1 (1991): 199–215. http://dx.doi.org/10.1215/s0012-7094-91-06309-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Adomian, G. "Solution of the Thomas-Fermi equation." Applied Mathematics Letters 11, no. 3 (1998): 131–33. http://dx.doi.org/10.1016/s0893-9659(98)00046-9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Stefanescu, Ștefan, Daria-Ioana Vișa, Tiberiu Harko, and Gabriela Mocanu. "Gravitational collapse of Bose-Einstein condensate dark matter halos with logarithmic nonlinearity." Romanian Astronomical Journal 33, no. 1-2 (2023): 15–35. http://dx.doi.org/10.59277/roaj.2023.1-2.02.

Full text

Abstract:

"If dark matter is composed of massive bosons, a Bose-Einstein Condensation process must have occurred during the cosmological evolution. Therefore galactic dark matter may be in a form of a condensate, characterized by a strong self-interaction. One of the interesting forms of the self-interaction potential of the condensate dark matter is the logarithmic form. In the present work we investigate one of the astrophysical implications of the condensate dark matter with logarithmic self-interaction, namely, its gravitational collapse. To describe the condensate dark matter we use the Gross-Pitaevskii equation, and the Thomas-Fermi approximation. By using the hydrodynamic representation of the Gross-Pitaevskii equation we obtain the equation of state of the condensate, which has the form of the ideal gas equation of state, with the pressure proportional to the dark matter density. In the Thomas-Fermi approximation, the evolution equations of the condensate reduce to the classical continuity, and Euler equations of fluid dynamics. We obtain the equations of motion of the condensate radius in spherical symmetry, by assuming certain particular forms for the velocity and density of the condensate. The collapse time required for the formation of a stable macroscopic astrophysical object is obtained in an integral form, and explicit numerical estimations for the formation of astrophysical objects with masses ranging from 106M⊙ to 1012M⊙ are presented."

APA, Harvard, Vancouver, ISO, and other styles

9

Purushothaman, Ganesh, Ekambaram Chandrasekaran, John R. Graef, and Ethiraju Thandapani. "Oscillation of Third-Order Thomas–Fermi-Type Nonlinear Differential Equations with an Advanced Argument." Mathematics 12, no. 24 (2024): 3959. https://doi.org/10.3390/math12243959.

Full text

Abstract:

In this paper, the authors obtain some new sufficient conditions for the oscillation of all solutions of Thomas–Fermi-type third-order nonlinear differential equations with advanced argument of the form (a2(t)(a1(t)y′(t))′)′−q(t)yα(σ(t))=0, under the assumptions that ∫t0∞1a2(t)dt<∞ and ∫t0∞1a1(t)dt=∞. The results are achieved by transforming the equation into a canonical-type equation and then applying integral averaging techniques and the comparison method to obtain oscillation criteria for the transformed equation. This in turn will imply the oscillation of the original equation. Several examples are provided to illustrate the significance of the main results.

APA, Harvard, Vancouver, ISO, and other styles

10

Tavassoli Kajani, Majid, Adem Kılıçman, and Mohammad Maleki. "The Rational Third-Kind Chebyshev Pseudospectral Method for the Solution of the Thomas-Fermi Equation over Infinite Interval." Mathematical Problems in Engineering 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/537810.

Full text

Abstract:

We propose a pseudospectral method for solving the Thomas-Fermi equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on the rational third-kind Chebyshev pseudospectral method that is indeed a combination of Tau and collocation methods. This method reduces the solution of this problem to the solution of a system of algebraic equations. Comparison with some numerical solutions shows that the present solution is highly accurate.

APA, Harvard, Vancouver, ISO, and other styles

11

Patil, Dinkar P., Yashashri S. Suryawanshi, and Mohini D. Nehete. "Application of Soham Transform for Solving Mathematical Models Occurring in Health Science and Biotechnology." INTERNATIONAL JOURNAL OF MATHEMATICS, STATISTICS AND OPERATIONS RESEARCH 2, no. 2 (2022): 273–88. http://dx.doi.org/10.47509/ijmsor.2022.v02i02.11.

Full text

Abstract:

Lot of mathematical models including differential equations play important role in healthcare and biotechnology. One of them is Malthus model. This model was developed by Thomas Malthus, in his essay on world population growth and resource supply. Another interesting equation is Advection diffusion equation and Predator prey model. We use a integral transform called as Soham transform to obtain the solutions of these models which are important in biotechnology and health sciences.

APA, Harvard, Vancouver, ISO, and other styles

12

Ersoy, Ozlem, and Idris Dag. "The Exponential Cubic B-Spline Algorithm for Korteweg-de Vries Equation." Advances in Numerical Analysis 2015 (February 17, 2015): 1–8. http://dx.doi.org/10.1155/2015/367056.

Full text

Abstract:

The exponential cubic B-spline algorithm is presented to find the numerical solutions of the Korteweg-de Vries (KdV) equation. The problem is reduced to a system of algebraic equations, which is solved by using a variant of Thomas algorithm. Numerical experiments are carried out to demonstrate the efficiency of the suggested algorithm.

APA, Harvard, Vancouver, ISO, and other styles

13

Desaix, M., D. Anderson, and M. Lisak. "Variational approach to the Thomas–Fermi equation." European Journal of Physics 25, no. 6 (2004): 699–705. http://dx.doi.org/10.1088/0143-0807/25/6/001.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Korpusov, M. O. "Blowup Solutions of the Nonlinear Thomas Equation." Theoretical and Mathematical Physics 201, no. 1 (2019): 1457–67. http://dx.doi.org/10.1134/s0040577919100040.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

Esposito, Salvatore. "Majorana solution of the Thomas–Fermi equation." American Journal of Physics 70, no. 8 (2002): 852–56. http://dx.doi.org/10.1119/1.1484144.

Full text

APA, Harvard, Vancouver, ISO, and other styles

16

He, Ji-Huan. "Variational approach to the Thomas–Fermi equation." Applied Mathematics and Computation 143, no. 2-3 (2003): 533–35. http://dx.doi.org/10.1016/s0096-3003(02)00380-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Khan, Hina, and Hang Xu. "Series solution to the Thomas–Fermi equation." Physics Letters A 365, no. 1-2 (2007): 111–15. http://dx.doi.org/10.1016/j.physleta.2006.12.064.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Fernández, Francisco M., and John F. Ogilvie. "Approximate solutions to the Thomas-Fermi equation." Physical Review A 42, no. 1 (1990): 149–54. http://dx.doi.org/10.1103/physreva.42.149.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Granas, A., R. B. Guenther, and J. W. Lee. "A Note on the Thomas-Fermi Equation." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 61, no. 3-5 (2008): 204–5. http://dx.doi.org/10.1002/zamm.19810610311.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Biedenharn, L. C. "A remark on the thomas-fermi equation." International Journal of Quantum Chemistry 9, S9 (2009): 31–33. http://dx.doi.org/10.1002/qua.560090807.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Parand, Kourosh, Kobra Rabiei, and Mehdi Delkhosh. "An efficient numerical method for solving nonlinear Thomas-Fermi equation." Acta Universitatis Sapientiae, Mathematica 10, no. 1 (2018): 134–51. http://dx.doi.org/10.2478/ausm-2018-0012.

Full text

Abstract:

Abstract In this paper, the nonlinear Thomas-Fermi equation for neutral atoms by using the fractional order of rational Chebyshev functions of the second kind (FRC2), ${\rm{FU}}_{\rm{n}}^\alpha \left( {{\rm{t}},{\rm{L}}} \right)$ (t, L), on an unbounded domain is solved, where L is an arbitrary parameter. Boyd (Chebyshev and Fourier Spectral Methods, 2ed, 2000) has presented a method for calculating the optimal approximate amount of L and we have used the same method for calculating the amount of L. With the aid of quasilinearization and FRC2 collocation methods, the equation is converted to a sequence of linear algebraic equations. An excellent approximation solution of y(t), y′ (t), and y ′ (0) is obtained.

APA, Harvard, Vancouver, ISO, and other styles

22

Chaudhary, Harideo. "Application of Differential Equation to Population Growth." Tribhuvan University Journal 28, no. 1-2 (2013): 75–80. http://dx.doi.org/10.3126/tuj.v28i1-2.26218.

Full text

Abstract:

Thomas Malthus, an 18th century English scholar, observed an essay written in 1798 that the growth of the human population is fundamentally different from the growth of the food supply to feed that population. He wrote that the human population was growing geometrically [i.e. exponentially] while the food supply was growing arithmetically [i.e. linearly]. He concluded that left unchecked, it would only be a matter of time before the world's population would be too large to feed itself. The first growth model we examine in this module is the one Thomas Malthus referred to in his famous essay. Malthus' model is considered a more sophisticated model for the special case of world population.

APA, Harvard, Vancouver, ISO, and other styles

23

Kaldybek, F. N., and I. F. Spivak-Lavrov. "DERIVATION OF THE DIMENSIONAL THOMAS-FERMI EQUATION FOR THE THOMAS-FERMI ATOM MODEL." Vestnik of M. Kozybayev North Kazakhstan University, no. 2 (54) (July 7, 2022): 7–16. http://dx.doi.org/10.54596/2309-6977-2022-2-7-16.

Full text

Abstract:

This article presents a method for calculating the energies of the values of the set of electron-neutral atoms. In this case, the interaction of electrons other than the Coulomb bond of the nucleus makes an important contribution to energy. Quantitative calculation of the interaction of these interactions with the introduction of the theory of approximation in the framework of the Thomas-Fermi statistical model by the method of self-correction field is particularly inefficient for complex atoms. However, for complex atoms, the method of approximation is shown, and its essence lies in its simplicity. Among the various methods for systems consisting of the same number of particles, the statistical method derived from the Thomas-Fermi statistical model of the atom plays an important role. This method (E. Fermi, L. Thomas, 1927) is based on the fact that in complex atoms with a large number of electrons, most electrons have relatively large quantum numbers. In this case, a semi-classical approximation is used. As a result, the concept of "cells in phase space" can be used for the state of the individual electrons of the atom. This model has been developed by researchers over a long period of time and has led to a consistent, complete doctrine without the defects of previous models, for example, its field of application is wider than the original Thomas-Fermi.

APA, Harvard, Vancouver, ISO, and other styles

24

Monk, Peter, Joachim Schöberl, and Astrid Sinwel. "Hybridizing Raviart-Thomas Elements for the Helmholtz Equation." Electromagnetics 30, no. 1-2 (2010): 149–76. http://dx.doi.org/10.1080/02726340903485414.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Ovando, G., J. J. Peña, and J. Morales. "Effective mass Schrödinger equation with Thomas-Fermi potential." Journal of Physics: Conference Series 574 (January 21, 2015): 012108. http://dx.doi.org/10.1088/1742-6596/574/1/012108.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Liu, Chunxiao, and Shengfeng Zhu. "Laguerre pseudospectral approximation to the Thomas–Fermi equation." Journal of Computational and Applied Mathematics 282 (July 2015): 251–61. http://dx.doi.org/10.1016/j.cam.2015.01.004.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Bénilan †, Philippe, and Haïm Brezis. "Nonlinear problems related to the Thomas-Fermi equation." Journal of Evolution Equations 3, no. 4 (2003): 673–770. http://dx.doi.org/10.1007/s00028-003-0117-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Zhu, Shengfeng, Hancan Zhu, Qingbiao Wu, and Yasir Khan. "An adaptive algorithm for the Thomas–Fermi equation." Numerical Algorithms 59, no. 3 (2011): 359–72. http://dx.doi.org/10.1007/s11075-011-9494-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Laurenzi, Bernard J. "An analytic solution to the Thomas–Fermi equation." Journal of Mathematical Physics 31, no. 10 (1990): 2535–37. http://dx.doi.org/10.1063/1.528998.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Chan, C. Y., and S. W. Du. "A constructive method for the Thomas-Fermi equation." Quarterly of Applied Mathematics 44, no. 2 (1986): 303–7. http://dx.doi.org/10.1090/qam/856183.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

MacLeod, Allan J. "Chebyshev series solution of the Thomas-Fermi equation." Computer Physics Communications 67, no. 3 (1992): 389–91. http://dx.doi.org/10.1016/0010-4655(92)90047-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Yao, Baoheng. "A series solution to the Thomas–Fermi equation." Applied Mathematics and Computation 203, no. 1 (2008): 396–401. http://dx.doi.org/10.1016/j.amc.2008.04.050.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Friedman, M., A. Rabinovitch, Y. Rosenfeld, and R. Thieberger. "Thomas-Fermi equation with non-spherical boundary conditions." Journal of Computational Physics 70, no. 2 (1987): 284–94. http://dx.doi.org/10.1016/0021-9991(87)90183-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Rȩbilas, Krzysztof. "Thomas Precession and the Bargmann-Michel-Telegdi Equation." Foundations of Physics 41, no. 12 (2011): 1800–1809. http://dx.doi.org/10.1007/s10701-011-9579-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Theotokoglou, Efstathios E., Theodoros I. Zarmpoutis, and Ioannis H. Stampouloglou. "Closed-Form Solutions of the Thomas-Fermi in Heavy Atoms and the Langmuir-Blodgett in Current Flow ODEs in Mathematical Physics." Mathematical Problems in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/721637.

Full text

Abstract:

Two kinds of second-order nonlinear, ordinary differential equations (ODEs) appearing in mathematical physics are analyzed in this paper. The first one concerns the Thomas-Fermi (TF) equation, while the second concerns the Langmuir-Blodgett (LB) equation in current flow. According to a mathematical methodology recently developed, the exact analytic solutions of both TF and LB ODEs are proposed. Both of these are nonlinear of the second order and by a series of admissible functional transformations are reduced to Abel’s equations of the second kind of the normal form. The closed form solutions of the TF and LB equations in the phase and physical plane are given. Finally a new interesting result has been obtained related to the derivative of the TF function at the limit.

APA, Harvard, Vancouver, ISO, and other styles

36

Gopalakrishnan, Jayadeep. "A Schwarz Preconditioner for a Hybridized Mixed Method." Computational Methods in Applied Mathematics 3, no. 1 (2003): 116–34. http://dx.doi.org/10.2478/cmam-2003-0009.

Full text

Abstract:

AbstractIn this paper, we provide a Schwarz preconditioner for the hybridized versions of the Raviart-Thomas and Brezzi-Douglas-Marini mixed methods. The preconditioner is for the linear equation for Lagrange multipliers arrived at by eliminating the flux as well as the primal variable. We also prove a condition number estimate for this equation when no preconditioner is used. Although preconditioners for the lowest-order case of the Raviart-Thomas method have been constructed previously by exploiting its connection with a nonconforming method, our approach is different in that we use a new variational characterization of the Lagrange multiplier equation. This allows us to precondition even the higher-order cases of these methods.

APA, Harvard, Vancouver, ISO, and other styles

37

Issakhov, Alibek, and Bakytzan Zhumagulov. "Numerical Modelling of the Thermal Process in the Aquatic Environment." Advanced Materials Research 787 (September 2013): 669–74. http://dx.doi.org/10.4028/www.scientific.net/amr.787.669.

Full text

Abstract:

This paper presents the mathematical model of the thermal influence to the aquatic environment of thermal power plant, which is solved by the Navier-Stokes and temperature equations for an incompressible fluid in a stratified medium. Numerical algorithm based on the projection method which solved with fractional step method. Three dimensional Poisson equation solved with Fourier method with combination of tridiagonal matrix method (Thomas algorithm).

APA, Harvard, Vancouver, ISO, and other styles

38

Jaros, Jaroslav, and Takaŝi Kusano. "On Avakumovic’s theorem for generalized Thomas-Fermi differential equations." Publications de l'Institut Math?matique (Belgrade) 99, no. 113 (2016): 125–37. http://dx.doi.org/10.2298/pim1613125j.

Full text

Abstract:

For the generalized Thomas-Fermi differential equation (|x?|??1x?)? = q(t)|x|??1x, it is proved that if 1 ? ? < ? and q(t) is a regularly varying function of index ? with ? > ?? ? 1, then all positive solutions that tend to zero as t ? 1 are regularly varying functions of one and the same negative index p and their asymptotic behavior at infinity is governed by the unique definite decay law. Further, an attempt is made to generalize this result to more general quasilinear differential equations of the form (p(t)|x?|??1x?)? = q(t)|x|??1x.

APA, Harvard, Vancouver, ISO, and other styles

39

Bhattacharyya, K., MS Uddin, and GC Layek. "Application of Scaling Group of Transformations to Steady Boundary Layer Flow of Newtonian Fluid over a Stretching Sheet in Presence of Chemically Reactive Species." Journal of Bangladesh Academy of Sciences 35, no. 1 (2011): 43–50. http://dx.doi.org/10.3329/jbas.v35i1.7969.

Full text

Abstract:

This investigation analyses application of Lies scaling group of transformations to steady flow of a Newtonian fluid over a stretching sheet in presence of chemically reactive species with first order reaction. The governing partial differential equations reduced to self-similar nonlinear ordinary differential equations by the transformations. Obtained momentum equation is solved analytically and the concentration equation is numerically solved applying finite difference method with Thomas algorithm. The plotted results reveal that with the increase of Schmidt number as well as reaction-rate parameter causes a reduction in the thickness of the concentration boundary layer and also the concentration at a point decreases.DOI: http://dx.doi.org/10.3329/jbas.v35i1.7969Journal of Bangladesh Academy of Sciences, Vol.35, No.1, 43-50, 2011

APA, Harvard, Vancouver, ISO, and other styles

40

Mavrin, Aleksey A., and Alexander V. Demura. "Approximate Solution of the Thomas–Fermi Equation for Free Positive Ions." Atoms 9, no. 4 (2021): 87. http://dx.doi.org/10.3390/atoms9040087.

Full text

Abstract:

The approximate solution of the nonlinear Thomas–Fermi (TF) equation for ions is found by the Fermi method. The solution is based on the new asymptotic representation of the TF ion size valid for any ionization degree. The two universal functions and their derivatives, introduced by Fermi, are calculated by recent effective algorithms for the Emden–Fowler type equations with the accuracy sufficient for majority of applications. The comparison of our results with those obtained previously shows high accuracy and validity for arbitrary values of ionization degree. This study could potentially be of interest for the statistical TF method applications in physics and chemistry.

APA, Harvard, Vancouver, ISO, and other styles

41

Dmytriv, V., Z. Stotsko, and I. Dmytriv. "Simulation of boundary layer under laminar and turbulent modes of newtonian fluid motion in a flexible pipeline." Technological Complexes 16 (December 5, 2019): 73–84. http://dx.doi.org/10.36910/2312-0584-16-2019-008.

Full text

Abstract:

The article deals with the modeling of boundary layer parameters for Newtonian fluids under laminar and turbulent modes of motion. Based on the system of Prandtl equations and initial boundary conditions under laminar motion, using the Gallorkin method, a tri-diagonal system of equations is formed, which connects the values of functions at the node of nets n+1 across the boundary layer. The numerical method uses the Thomas algorithm to calculate values Ujn+. The velocity value Vjn+1 is determined from the continuity equation by integration across the boundary layer. The Navier-Stokes equation in dimensionless form was used to model the turbulent boundary layer, given the velocity U is an independent variable. The differential equation system was solved using the numerical Dorodnicin method. The results of modeling the velocity distribution in the boundary layer, the thickness of the boundary layer in the section of the flexible pipeline 0.8-1.5 m from the beginning of the fluid entering the pipeline at the expense up to 0.1 kg/s are presented. Keywords: boundary layer, turbulent mode, velocity, Prandtl equation

APA, Harvard, Vancouver, ISO, and other styles

42

KARABULUT, Utku Cem, and Turgay KÖROĞLU. "Rasyonel Üslü Cebirsel ve Üstel Eşleme Yaklaşımı ile Thomas-Fermi Denklemi için İkinci Derece Doğruluklu Sonlu Farklar Yöntemi." Afyon Kocatepe University Journal of Sciences and Engineering 23, no. 3 (2023): 628–37. http://dx.doi.org/10.35414/akufemubid.1150843.

Full text

Abstract:

Many problems based on natural sciences need to be solved by the scientists and engineers to serve the humanity. One of the well-known model in atomic universe is condensed into an equation, and called the Thomas-Fermi equation. It is a second order differential equation, which describes charge distributions of heavy, neutral atoms. No exact analytical solution has been found for the equation yet. In fact, strong nonlinearity, singular character and unbounded interval of the problem causes great difficulty to obtain an approximate numerical solution as well. In this paper, the Thomas-Fermi equation is solved using a second order finite difference method along with application of quasi-linearization method. Semi-infinite interval of the problem is converted into [0, 1) using two different coordinate transformations, namely algebraic and exponential mapping. Numerical order of accuracy has been checked using systematic mesh refinements and comparing the calculated initial slope y'(0). Calculated results for initial slope is found in good agreement with the results available in the literature. Lastly, accuracy is improved by the application of the Richardson extrapolation.

APA, Harvard, Vancouver, ISO, and other styles

43

Franco, A. T., and C. O. R. Negrão. "INDOOR AIR TEMPERATURE DISTRIBUTION AN ALTERNATIVE APPROACH TO BUILDING SIMULATION." Revista de Engenharia Térmica 2, no. 1 (2003): 19. http://dx.doi.org/10.5380/reterm.v2i1.3514.

Full text

Abstract:

The current paper presents a model to predict indoor air temperature distribution. The approach is based on the energy conservation equation which is written for a certain number of finite volumes within the flow domain. The magnitude of the flow is estimated from a scale analysis of the momentum conservation equation. Discretized two or three-dimensional domains provide a set of algebraic equations. The resulting set of non-linear equations is iteratively solved using the line-by-line Thomas Algorithm. As long as the only equation to be solved is the conservation of energy and its coefficients are not strongly dependent on the temperature field, the solution is considerably fast. Therefore, the application of such model to a whole building system is quite reasonable. Two case studies involving buoyancy driven flows were carried out and comparisons with CFD solutions were performed. The results are quite promising for cases involving relatively strong couplings between heat and airflow.

APA, Harvard, Vancouver, ISO, and other styles

44

Parker, G. W. "Numerical solution of the Thomas-Fermi equation for molecules." Physical Review A 38, no. 5 (1988): 2205–10. http://dx.doi.org/10.1103/physreva.38.2205.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Leung, Y. C., and Shou-yong Pei. "High-density expansions of the relativistic Thomas-Fermi equation." Physical Review A 40, no. 5 (1989): 2731–37. http://dx.doi.org/10.1103/physreva.40.2731.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Ölschläger, M., G. Wirth, C. Morais Smith, and A. Hemmerich. "Kinetic Thomas–Fermi solutions of the Gross–Pitaevskii equation." Optics Communications 282, no. 7 (2009): 1472–77. http://dx.doi.org/10.1016/j.optcom.2008.12.054.

Full text

APA, Harvard, Vancouver, ISO, and other styles

47

Liao, Shijun. "An explicit analytic solution to the Thomas–Fermi equation." Applied Mathematics and Computation 144, no. 2-3 (2003): 495–506. http://dx.doi.org/10.1016/s0096-3003(02)00423-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Parand, K., and M. Shahini. "Rational Chebyshev pseudospectral approach for solving Thomas–Fermi equation." Physics Letters A 373, no. 2 (2009): 210–13. http://dx.doi.org/10.1016/j.physleta.2008.10.044.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

Baker, George A., and J. D. Johnson. "General structure of the Thomas-Fermi equation of state." Physical Review A 44, no. 4 (1991): 2271–83. http://dx.doi.org/10.1103/physreva.44.2271.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Robin, W. "Another rational analytical approximation to the Thomas-Fermi equation." Journal of Innovative Technology and Education 5, no. 1 (2018): 7–13. http://dx.doi.org/10.12988/jite.2018.823.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Journal articles on the topic 'Thomas equation'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles