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Relevant bibliographies by topics / Heat equation Numerical solutions

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Academic literature on the topic 'Heat equation Numerical solutions'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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Journal articles on the topic "Heat equation Numerical solutions"

1

Kafle, J., L. P. Bagale, and D. J. K. C. "Numerical Solution of Parabolic Partial Differential Equation by Using Finite Difference Method." Journal of Nepal Physical Society 6, no. 2 (December 31, 2020): 57–65. http://dx.doi.org/10.3126/jnphyssoc.v6i2.34858.

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In the real world, many physical problems like heat equation, wave equation, Laplace equation and Poisson equation are modeled by partial differential equations (PDEs). A PDE of the form ut = α uxx, (α > 0) where x and t are independent variables and u is a dependent variable; is a one-dimensional heat equation. This is an example of a prototypical parabolic equation. The heat equation has analytic solution in regular shape domain. If the domain has irregular shape, computing analytic solution of such equations is difficult. In this case, we can use numerical methods to compute the solution

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Tadeu, A., C. S. Chen, J. António, and Nuno Simões. "A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform." Advances in Applied Mathematics and Mechanics 3, no. 5 (October 2011): 572–85. http://dx.doi.org/10.4208/aamm.10-m1039.

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AbstractFourier transform is applied to remove the time-dependent variable in the diffusion equation. Under non-harmonic initial conditions this gives rise to a non-homogeneous Helmholtz equation, which is solved by the method of fundamental solutions and the method of particular solutions. The particular solution of Helmholtz equation is available as shown in [4, 15]. The approximate solution in frequency domain is then inverted numerically using the inverse Fourier transform algorithm. Complex frequencies are used in order to avoid aliasing phenomena and to allow the computation of the stati

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Korpinar, Zeliha. "On numerical solutions for the Caputo-Fabrizio fractional heat-like equation." Thermal Science 22, Suppl. 1 (2018): 87–95. http://dx.doi.org/10.2298/tsci170614274k.

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In this article, Laplace homotopy analysis method in order to solve fractional heat-like equation with variable coefficients, are introduced. Laplace homotopy analysis method, founded on combination of homotopy methods and Laplace transform is used to supply a new analytical approximated solutions of the fractional partial differential equations in case of the Caputo-Fabrizio. The solutions obtained are compared with exact solutions of these equations. Reliability of the method is given with graphical consequens and series solutions. The results show that the method is a powerfull and efficien

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Edja, Kouame Beranger, Kidjegbo Augustin Toure, and Brou Jean-Claude Koua. "Numerical Blow-up for A Heat Equation with Nonlinear Boundary Conditions." Journal of Mathematics Research 10, no. 5 (September 6, 2018): 119. http://dx.doi.org/10.5539/jmr.v10n5p119.

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We study numerical approximations of solutions of a heat equation with nonlinear boundary conditions which produce blow-up of the solutions. By a semidiscretization using a finite difference scheme in the space variable we get a system of ordinary differential equations which is an approximation of the original problem. We obtain sufficient conditions which guarantee the blow-up solution of this system in a finite time. We also show that this blow-up time converges to the theoretical one when the mesh size goes to zero. We present some numerical results to illustrate certain point of our work.

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Kochneff, Elizabeth, Yoram Sagher, and Kecheng Zhou. "Homogeneous solutions of the heat equation." Journal of Approximation Theory 69, no. 1 (April 1992): 35–47. http://dx.doi.org/10.1016/0021-9045(92)90047-r.

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Zhang, K. "On coupling between the Poincaré equation and the heat equation: non-slip boundary condition." Journal of Fluid Mechanics 284 (February 10, 1995): 239–56. http://dx.doi.org/10.1017/s0022112095000346.

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In contrast to the well-known columnar convection mode in rapidly rotating spherical fluid systems, the viscous dissipation of the preferred convection mode at sufficiently small Prandtl numberPrtakes place only in the Ekman boundary layer. It follows that different types of velocity boundary condition lead to totally different forms of the asymptotic relationship between the Rayleigh numberRand the Ekman numberEfor the onset of convection. We extend both perturbation and numerical analyses with the stress-free boundary condition (Zhang 1994) in rapidly rotating spherical systems to those with

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Agyeman, Edmund, and Derick Folson. "Algorithm Analysis of Numerical Solutions to the Heat Equation." International Journal of Computer Applications 79, no. 5 (October 18, 2013): 11–19. http://dx.doi.org/10.5120/13736-1535.

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Čiegis, Raimondas. "NUMERICAL SOLUTION OF HYPERBOLIC HEAT CONDUCTION EQUATION." Mathematical Modelling and Analysis 14, no. 1 (March 31, 2009): 11–24. http://dx.doi.org/10.3846/1392-6292.2009.14.11-24.

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Hyperbolic heat conduction problem is solved numerically. The explicit and implicit Euler schemes are constructed and investigated. It is shown that the implicit Euler scheme can be used to solve efficiently parabolic and hyperbolic heat conduction problems. This scheme is unconditionally stable for both problems. For many integration methods strong numerical oscillations are present, when the initial and boundary conditions are discontinuous for the hyperbolic problem. In order to regularize the implicit Euler scheme, a simple linear relation between time and space steps is proposed, which au

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Mhammad, Aree A., Faraidun K. Hama Salh, and Najmadin W. Abdulrahman. "Numerical Solution for Non-Stationary Heat Equation in Cooling of Computer Radiator System." Journal of Zankoy Sulaimani - Part A 12, no. 1 (November 5, 2008): 97–102. http://dx.doi.org/10.17656/jzs.10199.

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Kandel, H. P., J. Kafle, and L. P. Bagale. "Numerical Modelling on the Influence of Source in the Heat Transformation: An Application in the Metal Heating for Blacksmithing." Journal of Nepal Physical Society 7, no. 2 (August 6, 2021): 97–101. http://dx.doi.org/10.3126/jnphyssoc.v7i2.38629.

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Many physical problems, such as heat transfer and wave transfer, are modeled in the real world using partial differential equations (PDEs). When the domain of such modeled problems is irregular in shape, computing analytic solution becomes difficult, if not impossible. In such a case, numerical methods can be used to compute the solution of such PDEs. The Finite difference method (FDM) is one of the numerical methods used to compute the solutions of PDEs by discretizing the domain into a finite number of regions. We used FDMs to compute the numerical solutions of the one dimensional heat equat

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Dissertations / Theses on the topic "Heat equation Numerical solutions"

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Hayman, Kenneth John. "Finite-difference methods for the diffusion equation." Title page, table of contents and summary only, 1988. http://web4.library.adelaide.edu.au/theses/09PH/09phh422.pdf.

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Sweet, Erik. "ANALYTICAL AND NUMERICAL SOLUTIONS OF DIFFERENTIALEQUATIONS ARISING IN FLUID FLOW AND HEAT TRANSFER PROBLEMS." Doctoral diss., University of Central Florida, 2009. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/2585.

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The solutions of nonlinear ordinary or partial differential equations are important in the study of fluid flow and heat transfer. In this thesis we apply the Homotopy Analysis Method (HAM) and obtain solutions for several fluid flow and heat transfer problems. In chapter 1, a brief introduction to the history of homotopies and embeddings, along with some examples, are given. The application of homotopies and an introduction to the solutions procedure of differential equations (used in the thesis) are provided. In the chapters that follow, we apply HAM to a variety of problems to highlight its

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Sweet, Erik. "Analytical and numerical solutions of differential equations arising in fluid flow and heat transfer problems." Orlando, Fla. : University of Central Florida, 2009. http://purl.fcla.edu/fcla/etd/CFE0002889.

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Brubaker, Lauren P. "Completely Residual Based Code Verification." University of Akron / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=akron1132592325.

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Al-Jawary, Majeed Ahmed Weli. "The radial integration boundary integral and integro-differential equation methods for numerical solution of problems with variable coefficients." Thesis, Brunel University, 2012. http://bura.brunel.ac.uk/handle/2438/6449.

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The boundary element method (BEM) has become a powerful method for the numerical solution of boundary-value problems (BVPs), due to its ability (at least for problems with constant coefficients) of reducing a BVP for a linear partial differential equation (PDE) defined in a domain to an integral equation defined on the boundary, leading to a simplified discretisation process with boundary elements only. On the other hand, the coefficients in the mathematical model of a physical problem typically correspond to the material parameters of the problem. In many physical problems, the governing equa

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Ferreira, Fábio Freitas. "Problemas inversos sobre a esfera." Universidade do Estado do Rio de Janeiro, 2008. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=889.

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Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro<br>O objetivo desta tese é o desenvolvimento de algoritmos para determinar as soluções, e para determinação de fontes, das equações de Poisson e da condução de calor definidas em uma esfera. Determinamos as formas das equações de Poisson e de calor sobre a esfera, e desenvolvemos métodos iterativos, baseados em uma malha icosaedral e sua respectiva malha dual, para obter as soluções das mesmas. Mostramos que os métodos iterativos convergem para as soluções das equações discretizadas. Empregamos o método de regulariza

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Simmel, Martin. "Two numerical solutions for the stochastic collection equation." Universitätsbibliothek Leipzig, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-215378.

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Two different methods are used to solve the stochastic collection equation (SCE) numerically. They are called linear discrete method (LDM) and bin shift method (BSM), respectively. Conceptually, both of them are similar to the well-known discrete method (DM) of Kovetz and Olund. For LDM and BSM, their concept is extended to two prognostic moments. Therefore, the \"splitting factors\" (which are constant in time for DM) become time-dependent for LDM and BSM. Simulations are shown for the Golovin kernel (for which an analytical solution is available) and the hydrodynamic kernel after Hall. Diffe

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Simmel, Martin. "Two numerical solutions for the stochastic collection equation." Wissenschaftliche Mitteilungen des Leipziger Instituts für Meteorologie ; 17 = Meteorologische Arbeiten aus Leipzig ; 5 (2000), S. 61-73, 2000. https://ul.qucosa.de/id/qucosa%3A15149.

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Two different methods are used to solve the stochastic collection equation (SCE) numerically. They are called linear discrete method (LDM) and bin shift method (BSM), respectively. Conceptually, both of them are similar to the well-known discrete method (DM) of Kovetz and Olund. For LDM and BSM, their concept is extended to two prognostic moments. Therefore, the \"splitting factors\" (which are constant in time for DM) become time-dependent for LDM and BSM. Simulations are shown for the Golovin kernel (for which an analytical solution is available) and the hydrodynamic kernel after Hall. Diffe

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Sjölander, Filip. "Numerical solutions to the Boussinesq equation and the Korteweg-de Vries equation." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-297544.

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The aim of the report is to numerically construct solutions to two analytically solvable non-linear differential equations: the Korteweg–De Vries equation and the Boussinesq equation. To accomplish this, a range of numerical methods where implemented, including Galerkin methods. To asses the accuracy of the solutions, analytic solutions were derived for reference. Characteristic of both equations is that they support a certain type of wave-solutions called "soliton solutions", which admit an intuitive physical interpretation as solitary traveling waves. Theses solutions are the ones simulated.

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Sundqvist, Per. "Numerical Computations with Fundamental Solutions." Doctoral thesis, Uppsala : Acta Universitatis Upsaliensis : Univ.-bibl. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5757.

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Books on the topic "Heat equation Numerical solutions"

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Bamberger, Alain. Analyse, optimisation et filtrage numériques: Anaylse numérique de l'équation de la chaleur. [Palaiseau, France]: Ecole polytechnique, Département de mathématiques appliquées, 1991.

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2

Day, William Alan. Heat conduction within linear thermoelasticity. New York: Springer-Verlag, 1985.

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3

N, Dewynne Jeffrey, ed. Heat conduction. Oxford [Oxfordshire]: Blackwell Scientific Publications, 1987.

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4

Ishii, Audrey L. A numerical solution for the diffusion equation in hydrogeologic systems. Urbana, Ill: Dept. of the Interior, U.S. Geological Survey, 1989.

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Ishii, Audrey L. A numerical solution for the diffusion equation in hydrogeologic systems. Urbana, Ill: Dept. of the Interior, U.S. Geological Survey, 1989.

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Ishii, Audrey L. A numerical solution for the diffusion equation in hydrogeologic systems. Urbana, Ill: Dept. of the Interior, U.S. Geological Survey, 1989.

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7

Introduction to Monte Carlo methods for transport and diffusion equations. Oxford: Oxford University Press, 2003.

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The energy method, stability, and nonlinear convection. 2nd ed. New York: Springer, 2004.

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9

The energy method, stability, and nonlinear convection. New York: Springer-Verlag, 1992.

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10

Inverse Stefan problems. Dordrecht: Kluwer Academic Publishers, 1997.

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Book chapters on the topic "Heat equation Numerical solutions"

1

Saitoh, Saburou. "Inequalities for the solutions of the heat equation." In International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, 351–59. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-7565-3_27.

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Hintermüller, M., S. Volkwein, and F. Diwoky. "Fast Solution Techniques in Constrained Optimal Boundary Control of the Semilinear Heat Equation." In International Series of Numerical Mathematics, 119–47. Basel: Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-7721-2_6.

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3

John, Fritz. "Numerical solution of the equation of heat conduction for preceding times." In Fritz John, 389–402. Boston, MA: Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4612-5406-5_30.

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John, Fritz. "Numerical solution of the equation of heat conduction for preceding times." In Fritz John, 389–402. Boston, MA: Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4612-5409-6_30.

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Keller, Joseph B., and John S. Lowengrub. "Asymptotic and Numerical Results for Blowing-Up Solutions to Semilinear Heat Equations." In Singularities in Fluids, Plasmas and Optics, 111–29. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2022-7_8.

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Bouchon, François, and Gunther H. Peichl. "An Immersed Interface Technique for the Numerical Solution of the Heat Equation on a Moving Domain." In Numerical Mathematics and Advanced Applications 2009, 181–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11795-4_18.

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Koleva, Miglena N. "Numerical Solution of the Heat Equation in Unbounded Domains Using Quasi-uniform Grids." In Large-Scale Scientific Computing, 509–17. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11666806_58.

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Anastassiou, George A. "Optimal Estimate for the Numerical Solution of Multidimensional Dirichlet Problem for the Heat Equation." In Intelligent Mathematics: Computational Analysis, 749–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-17098-0_45.

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Lachaab, Mohamed, Peter R. Turner, and Athanassios S. Fokas. "Numerical Evaluation of Fokas’ Transform Solution of the Heat Equation on the Half-Line." In Advanced Computing in Industrial Mathematics, 245–56. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97277-0_20.

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Lisik, Zbigniew, Janusz Wozny, Malgorzata Langer, and Niccolò Rinaldi. "Analytical Solutions of the Diffusive Heat Equation as the Application for Multi-cellular Device Modeling – A Numerical Aspect." In Computational Science - ICCS 2004, 1021–28. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-25944-2_132.

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Conference papers on the topic "Heat equation Numerical solutions"

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Kazakov, A. L., and L. F. Spevak. "Numerical study of travelling wave type solutions for the nonlinear heat equation." In MECHANICS, RESOURCE AND DIAGNOSTICS OF MATERIALS AND STRUCTURES (MRDMS-2019): Proceedings of the 13th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures. AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5135130.

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Zhang, Juntao, and Raj M. Manglik. "Numerical Investigation of Single Bubble Dynamics During Nucleate Boiling in Aqueous Surfactant Solutions." In ASME 2003 Heat Transfer Summer Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/ht2003-47047.

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The dynamics of a single growing and departing bubble during nucleate boiling from a horizontal heated surface in an aqueous surfactant solution has been numerically simulated. The full Navier-Stokes equations together with the bulk transport and adsorption-desorption-controlled surfactant interfacial transport equations are solved. A PDE-based fast local level-set method is used to computationally capture the vapor-liquid interface, and the dynamic surface tension is modeled as a body force on the interface. A second-order projection method along with a third-order ENO (essentially non-oscill

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Shibata, Daisuke, and Takayuki Utsumi. "Numerical Solutions of Poisson Equation by the CIP-Basis Set Method." In ASME 2009 InterPACK Conference collocated with the ASME 2009 Summer Heat Transfer Conference and the ASME 2009 3rd International Conference on Energy Sustainability. ASMEDC, 2009. http://dx.doi.org/10.1115/interpack2009-89150.

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An accurate and reliable real space method for the ab initio calculation of electronic-structures of materials has been desired. Historically, the most popular method in this field has been the Plane Wave method. However, because the basis functions of the Plane Wave method are not local in real space, it is inefficient to represent the highly localized inner-shell electron state and it generally give rise to a large dense potential matrix which is difficult to deal with. Moreover, it is not suitable for parallel computers, because it requires Fourier transformations. These limitations of the

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Raszkowski, Tomasz, Mariusz Zubert, Marcin Janicki, and Andrzej Napieralski. "Numerical solution of 1-D DPL heat transfer equation." In 2015 MIXDES - 22nd International Conference "Mixed Design of Integrated Circuits & Systems". IEEE, 2015. http://dx.doi.org/10.1109/mixdes.2015.7208558.

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Malkov, Eugene, and Michail Ivanov. "Numerical Solution of the Boltzmann Equation in Divergent Form." In 10th AIAA/ASME Joint Thermophysics and Heat Transfer Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2010. http://dx.doi.org/10.2514/6.2010-4503.

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Jannelli, Alessandra, Marianna Ruggieri, and Maria Paola Speciale. "Numerical solutions of space-fractional advection-diffusion equation with a source term." In INTERNATIONAL YOUTH SCIENTIFIC CONFERENCE “HEAT AND MASS TRANSFER IN THE THERMAL CONTROL SYSTEM OF TECHNICAL AND TECHNOLOGICAL ENERGY EQUIPMENT” (HMTTSC 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5114290.

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Qubeissi, Mansour al. "Proposing a Numerical Solution for the 3D Heat Conduction Equation." In 2012 6th Asia Modelling Symposium (AMS 2012). IEEE, 2012. http://dx.doi.org/10.1109/ams.2012.10.

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Zureigat, Hamzeh H., and Ahmad Izani Md Ismail. "Numerical solution of fuzzy heat equation with two different fuzzifications." In 2016 SAI Computing Conference (SAI). IEEE, 2016. http://dx.doi.org/10.1109/sai.2016.7555966.

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Tarmizi, Tarmizi, Evi Safitri, Said Munzir, and Marwan Ramli. "On the numerical solutions of a one-dimensional heat equation: Spectral and Crank Nicolson method." In THE 4TH INDOMS INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATION (IICMA 2019). AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0017131.

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Kurokawa, Fa´bio Yukio, Antonio Joa˜o Diniz, and Joa˜o Batista Campos-Silva. "Analytical/Numerical Hybrid Solution for One-Dimensional Ablation Problem." In ASME 2003 Heat Transfer Summer Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/ht2003-47174.

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Ablation is a thermal protection process with several applications in engineering, mainly in the field of airspace industry. The use of conventional materials must be quite restricted, because they would suffer catastrophic flaws due to thermal degradation of their structures. However, the same materials can be quite suitable once being protected by well-known ablative materials. The process that involves the ablative phenomena is complex, could involve the whole or partial loss of material that is sacrificed for absorption of energy. The analysis of the ablative process in a blunt body with r

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Reports on the topic "Heat equation Numerical solutions"

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Chang, B. Analytical Solutions for Testing Ray-Effect Errors in Numerical Solutions of the Transport Equation. Office of Scientific and Technical Information (OSTI), May 2003. http://dx.doi.org/10.2172/15004539.

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