Готові списки джерел за темами / Numerical and computational mathematics

Добірка наукової літератури з теми "Numerical and computational mathematics"

Автор: Grafiati
Опубліковано: 10 грудня 2022
Оновлено: 28 січня 2023

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Статті в журналах з теми "Numerical and computational mathematics"

1

Planitz, Max, and T. R. F. Nonweiler. "Computational Mathematics: An Introduction to Numerical Approximation." Mathematical Gazette 69, no. 447 (March 1985): 67. http://dx.doi.org/10.2307/3616478.

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2

Wimp, Jet, and T. R. F. Nonweiler. "Computational Mathematics, An Introduction to Numerical Approximation." Mathematics of Computation 46, no. 174 (April 1986): 761. http://dx.doi.org/10.2307/2008016.

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3

Temirgaliyev, N., and A. Zhubanysheva. "Approximation Theory, Computational Mathematics and Numerical Analysis in new conception of Computational (Numerical) Diameter." BULLETIN of the L.N. Gumilyov Eurasian National University. MATHEMATICS.COMPUTER SCIENCE. MECHANICS Series 124, no. 3 (2018): 8–88. http://dx.doi.org/10.32523/2616-7182/2018-124-3-8-88.

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4

G., W., Gunther Hammerlin, Karl-Heinz Hoffmann, and Larry Schumaker. "Numerical Mathematics." Mathematics of Computation 58, no. 198 (April 1992): 855. http://dx.doi.org/10.2307/2153223.

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Cook, Gregory B., and Saul A. Teukolsky. "Numerical relativity: challenges for computational science." Acta Numerica 8 (January 1999): 1–45. http://dx.doi.org/10.1017/s0962492900002889.

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We describe the burgeoning field of numerical relativity, which aims to solve Einstein's equations of general relativity numerically. The field presents many questions that may interest numerical analysts, especially problems related to nonlinear partial differential equations: elliptic systems, hyperbolic systems, and mixed systems. There are many novel features, such as dealing with boundaries when black holes are excised from the computational domain, or how even to pose the problem computationally when the coordinates must be determined during the evolution from initial data. The most important unsolved problem is that there is no known general 3-dimensional algorithm that can evolve Einstein's equations with black holes that is stable. This review is meant to be an introduction that will enable numerical analysts and other computational scientists to enter the field. No previous knowledge of special or general relativity is assumed.
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6

Vabishchevich, P. N. "Works of A.A. Samarskii on Computational Mathematics." Computational Methods in Applied Mathematics 9, no. 1 (2009): 5–36. http://dx.doi.org/10.2478/cmam-2009-0002.

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Abstract This is a review of the main results in computational mathematics that were obtained by the eminent Russian mathematician Alexander Andreevich Samarskii (February 19, 1919 – February 11, 2008). His outstanding research output addresses all the main questions that arise in the construction and justification of algorithms for the numerical solution of problems from mathematical physics. The remarkable works of A.A. Samarskii include statements of the main principles re- quired in the construction of difference schemes, rigorous mathematical proofs of the stability and convergence of these schemes, and also investigations of their algorith- mic implementation. A.A. Samarskii and his collaborators constructed and applied in practical calculations a large number of algorithms for solving various problems from mathematical physics, including thermal physics, gas dynamics, magnetic gas dynam- ics, plasma physics, ecology and other important models from the natural sciences.
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7

Kissane, Barry. "The Scientific Calculator and School Mathematics." Southeast Asian Mathematics Education Journal 6, no. 1 (December 27, 2016): 29–48. http://dx.doi.org/10.46517/seamej.v6i1.38.

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Scientific calculators are sometimes regarded as important only for obtaining numerical answers to computational questions, and thus in some countries regarded as inappropriate for school mathematics, lest they might undermine the school curriculum. This paper argues a contrary view that, firstly, numerical computation is not the principal purpose of scientific calculators in education, and secondly that calculators can play a valuable role in supporting students’ learning. Recent developments of calculators are outlined, noting that theirprincipal intention has been to make calculators easier to use, align their functionality with the school mathematics curriculum and represent mathematical expressions in conventional ways. A model for the educational use of calculators is described, with four key components:representation, computation, exploration and affirmation. Examples of how these might impact positively on school mathematics are presented, and suggestions are made regarding good pedagogy and curriculum with calculators in mind. The paper concludes that scientific calculators represent the best available technology to provide widespread access to some ICT in the mathematics curriculum for all students in the SEAMEO region.
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8

Braack, Malte, Dietmar Gallistl, Jun Hu, Guido Kanschat, and Xuejun Xu. "Sino–German Computational and Applied Mathematics." Computational Methods in Applied Mathematics 21, no. 3 (June 8, 2021): 497–99. http://dx.doi.org/10.1515/cmam-2021-0102.

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Abstract This short article serves as an epilog of the thirteen preceding papers in this special issue of CMAM. All contributions are authored by participants of the 7th Sino–German Workshop on Computational and Applied Mathematics at the Kiel University. The topics cover fourth-order problems, solvers and multilevel methods, a posteriori error control and adaptivity, and data science.
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9

Hoppe, Ronald H. W., Jun Hu, Malte A. Peter, Rolf Rannacher, Zhongci Shi, and Xuejun Xu. "Chinese–German Computational and Applied Mathematics." Computational Methods in Applied Mathematics 16, no. 4 (October 1, 2016): 605–8. http://dx.doi.org/10.1515/cmam-2016-0028.

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AbstractThis short article is the epilog of the 14 preceding papers in this and the previous issue of CMAM. All are extracted from the 5th Chinese–German Workshop on Computational and Applied Mathematics at Augsburg but submitted as individual papers to the journal.
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Smolensky, Paul. "Symbolic functions from neural computation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1971 (July 28, 2012): 3543–69. http://dx.doi.org/10.1098/rsta.2011.0334.

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Is thought computation over ideas? Turing, and many cognitive scientists since, have assumed so, and formulated computational systems in which meaningful concepts are encoded by symbols which are the objects of computation. Cognition has been carved into parts, each a function defined over such symbols. This paper reports on a research program aimed at computing these symbolic functions without computing over the symbols. Symbols are encoded as patterns of numerical activation over multiple abstract neurons, each neuron simultaneously contributing to the encoding of multiple symbols. Computation is carried out over the numerical activation values of such neurons, which individually have no conceptual meaning. This is massively parallel numerical computation operating within a continuous computational medium. The paper presents an axiomatic framework for such a computational account of cognition, including a number of formal results. Within the framework, a class of recursive symbolic functions can be computed. Formal languages defined by symbolic rewrite rules can also be specified, the subsymbolic computations producing symbolic outputs that simultaneously display central properties of both facets of human language: universal symbolic grammatical competence and statistical, imperfect performance.
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Дисертації з теми "Numerical and computational mathematics"

1

Baer, Lawrence H. "Numerical aspects of computational geometry." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=22507.

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This thesis is concerned with the numerical issues resulting from the implementation of geometric algorithms on finite precision digital computers. From an examination of the general problem and a survey of previous research, it appears that the central problem of numerical computational geometry is how to deal with degenerate and nearly degenerate input. For some applications, such as solid modeling, degeneracy is often intended but we cannot always ascertain its existence using finite precision. For other applications, degenerate input is unwanted but nearly degenerate input is unavoidable. Near degeneracy is associated with ill-conditioning of the input and can lead to a serious loss of accuracy and program failure. These observations lead us to a discussion of problem condition in the context of computational geometry. We use the Voronoi diagram construction problem as a case study and show that problem condition can also play a role in algorithm design.
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2

Djambazov, Georgi Stefanov. "Numerical techniques for computational aeroacoustics." Thesis, University of Greenwich, 1998. http://gala.gre.ac.uk/6149/.

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The problem of aerodynamic noise is considered following the Computational Aeroacoustics approach which is based on direct numerical simulation of the sound field. In the region of sound generation, the unsteady airflow is computed separately from the sound using Computational Fluid Dynamics (CFD) codes. Overlapping this region and extending further away is the acoustic domain where the linearised Euler equations governing the sound propagation in moving medium are solved numerically. After considering a finite volume technique of improved accuracy, preference is given to an optimised higher order finite difference scheme which is validated against analytical solutions of the governing equations. A coupling technique of two different CFD codes with the acoustic solver is demonstrated to capture the mechanism of sound generation by vortices hitting solid objects in the flow. Sub-grid turbulence and its effect 011sound generation has not been considered in this thesis. The contribution made to the knowledge of Computational Aeroacoustics can be summarised in the following: 1) Extending the order of accuracy of the staggered leap-frog method for the linearised Euler equations in both finite volume and finite difference formulations; 2) Heuristically determined optimal coefficients for the staggered dispersion relation preserving scheme; 3) A solution procedure for the linearised Euler equations involving mirroring at solid boundaries which combines the flexibility of the finite volume method with the higher accuracy of the finite difference schemes; 4) A method for identifying the sound sources in the CFD solution at solid walls and an expansion technique for sound sources inside the flow; 5) Better understanding of the three-level structure of the motions in air: mean flow, flow perturbations, and acoustic waves. It can be used, together with detailed simulation results, in the search for ways of reducing the aerodynamic noise generated by propellers, jets, wind turbines, tunnel exits, and wind-streamed buildings.
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Kuster, Christopher M. "Fast Numerical Methods for Evolving Interfaces." NCSU, 2006. http://www.lib.ncsu.edu/theses/available/etd-04262006-083221/.

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Free and/or moving boundary problems occur in a wide range of applications. These boundaries can obey either local or global conditions. In this dissertation, new numerical techniques for solving some of these problems are developed, analyzed, implemented and tested. The new techniques for free and moving boundary problems are 1) a second order method for solving moving boundary problems and 2) a hybrid level set/boundary element method for solving some free boundary problems. The main tool used in both is the Fast Marching method, a fast algorithm for solving the eikonal equation. An application using Fast Marching to solve a model for sand pile formation in domains with obstacles is shown. A new, second order Fast Marching scheme for domains with obstacles is introduced. We look at the stability and accuracy of discretizations commonly used with Fast Marching. The performance of Fast Marching is compared that of Fast Sweeping, another eikonal solver. The second order method for solving moving boundary problems is applied to some simple examples. Finally, a globally defined free boundary problem inspired by fluid dynamics, the Bernoulli problem, is solved using the hybrid method.
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4

Lindgren, Jonas. "Numerical modelling of district heating networks." Thesis, Umeå universitet, Institutionen för fysik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-143896.

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District heating is today, in Sweden, the most common method used for heating buildings in cities. More than half of all the buildings, both commercial and residential, are heated using district heating. The load on the district heating networks are affected by, among other things, the time of the day and different external conditions, such as temperature differences. One has to be able to simulate the heat and pressure losses in the network in order to deliver the amount of heat demanded by the customers. Expansions of district heating networks and disrupted pipes also demand good simulations of the networks. To cope with this, energy companies use simulation software. These software need to contain numerical methods that provide accurate and stable results and at the same time be fast and efficient. At the moment there are available software packages that works but these have some limitations. Among other things you may need to divide the whole network into smaller loops or try to guess how the distribution of pressure and flow in the network looks like. The development in recent years makes it possible to use better and more efficient algorithms for these types of problems. The purpose of this report is therefore to introduce a better and more efficient method than that used in the current situation. This work is the first step in order to replace a current method used in a simulation software provided by Vitec energy. Therefore, we will in this report, stick to computing pressure and flow in the network. The method we will introduce in this report is called the gradient method and it is based on the Newton Raphson method. Unlike with older methods like Hardy Cross which is a relaxation method, you do not have to divide the network into loops. Instead you create a matrix representation of the network that is used in the computations. The idea is also that you should not need to make good initial guesses to get the method to converge quickly. We performed a number of test simulations in order to examine how the method performs. We tested how different initial guesses and how different sizes of the networks affected the number of iterations. The results shows that the model is capable of solving large networks within a reasonable number of iterations. The results also show that the initial guesses have little impact on the number of iterations. Changing the initial guess on the pressure does not affect the number at all but it turns out that changing the initial guess on the flow can affect the number of iterations a little, but not much.
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5

Engblom, Stefan. "Numerical methods for the chemical master equation." Licentiate thesis, Uppsala : Univ. : Dept. of Information Technology, Univ, 2006. http://www.it.uu.se/research/publications/lic/2006-007/2006-007.pdf.

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Eliasson, Bengt. "Numerical simulation of kinetic effects in ionospheric plasma." Licentiate thesis, Uppsala : Dept. of Information Technology, Univ, 2001. http://www.it.uu.se/research/reports/lic/2001-004/2001-004-nc.pdf.

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Mitrouli, Marilena Th. "Numerical issues and computational problems in algebraic control theory." Thesis, City University London, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280573.

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Kormann, Katharina. "Numerical methods for quantum molecular dynamics." Licentiate thesis, Uppsala : Department of Information Technology, Uppsala University, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-108366.

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Bastounis, Alexander James. "On fundamental computational barriers in the mathematics of information." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/279086.

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This thesis is about computational theory in the setting of the mathematics of information. The first goal is to demonstrate that many commonly considered problems in optimisation theory cannot be solved with an algorithm if the input data is only known up to an arbitrarily small error (modelling the fact that most real numbers are not expressible to infinite precision with a floating point based computational device). This includes computing the minimisers to basis pursuit, linear programming, lasso and image deblurring as well as finding an optimal neural network given training data. These results are somewhat paradoxical given the success that existing algorithms exhibit when tackling these problems with real world datasets and a substantial portion of this thesis is dedicated to explaining the apparent disparity, particularly in the context of compressed sensing. To do so requires the introduction of a variety of new concepts, including that of a breakdown epsilon, which may have broader applicability to computational problems outside of the ones central to this thesis. We conclude with a discussion on future research directions opened up by this work.
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Berglund, André. "Numerical Simulations of Linear Stochastic Oscillators : driven by Wiener and Poisson processes." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-134800.

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The main component of this essay is the numerical analysis of stochastic differential equations driven by Wiener and Poisson processes. In order to do this, we focus on two model problems, the geometric Brownian motion and the linear stochastic oscillator, studied in the literature for stochastic differential equations only driven by a Wiener process. This essay covers theoretical as well as numerical investigations of jump - or more specifically, Poisson - processes and how they influence the above model problems.
Den huvudsakliga komponenten av uppsatsen är en numerisk analys av stokastiska differentialekvationer drivna av Wiener- och Poisson-processer. För att göra det så fokuserar vi på två modellproblem, den geometriska Brownska rörelsen samt den linjära stokastiska oscillatorn, studerade i litteratur för stokastiska differentialekvationer som bara drivs av en Wiener-process.Den här uppsatsen täcker teoretiska samt numeriska undersökningar av hopp - eller mer specifikt, Poisson - processer och hur de påverkar de ovan nämnda modellproblemen.
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Книги з теми "Numerical and computational mathematics"

1

A, Maron I., ed. Computational mathematics. Moscow: Mir Publishers, 1987.

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2

Mateos, Mariano, and Pedro Alonso, eds. Computational Mathematics, Numerical Analysis and Applications. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49631-3.

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3

Introduction to computational mathematics. Singapore: World Scientific Pub., 2008.

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4

1958-, Cucker Felipe, ed. Foundations of computational mathematics, Minneapolis 2002. Cambridge: Cambridge University Press, 2004.

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5

1958-, Cucker Felipe, Pinkus Allan 1946-, and Todd Michael J. 1947-, eds. Foundations of computational mathematics, Hong Kong 2008. Cambridge, UK: Cambridge University Press, 2009.

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6

Chris, Phillips. Computational numerical methods. Chichester [West Sussex]: Ellis Horwood, 1986.

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7

C, Misra J., ed. Computational mathematics, modelling, and algorithms. New Delhi: Narosa Pub. House, 2003.

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8

Langtangen, Hans Petter. Computational Partial Differential Equations: Numerical Methods and Diffpack Programming. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999.

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9

1937-, Yamamoto T., ed. Advances in computational mathematics: Proceedings of the International Symposium on Computational Mathematics, Matsuyama, Japan, 30 August-4 September 1990. Amsterdam: North-Holland, 1992.

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10

service), SpringerLink (Online, ed. Numerical Analysis. Boston: Springer Science+Business Media, LLC, 2012.

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Частини книг з теми "Numerical and computational mathematics"

1

Bauldry, William C. "Numerical Differentiation." In Introduction to Computational Mathematics, 70–83. Boca Raton: CRC Press, 2022. http://dx.doi.org/10.1201/9781003299257-4.

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Harris, John W., and Horst Stocker. "Numerical Computation (arithmetics and numerics)." In Handbook of Mathematics and Computational Science, 1–36. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-5317-4_1.

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Bauldry, William C. "V. Numerical Integration." In Introduction to Computational Mathematics, 117–39. Boca Raton: CRC Press, 2022. http://dx.doi.org/10.1201/9781003299257-7.

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Hairer, Ernst, and Gerhard Wanner. "Numerical Experiments." In Springer Series in Computational Mathematics, 143–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-05221-7_10.

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Hairer, Ernst, Gerhard Wanner, and Christian Lubich. "Numerical Integrators." In Springer Series in Computational Mathematics, 23–46. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-05018-7_2.

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Borthwick, David. "Numerical Computations." In Progress in Mathematics, 397–414. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-33877-4_16.

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Redfern, E. J. "Numerical Calculus." In Introduction to Pascal for Computational Mathematics, 106–17. London: Macmillan Education UK, 1987. http://dx.doi.org/10.1007/978-1-349-18977-9_9.

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Iserles, Arieh. "Numerical Analysis." In Encyclopedia of Applied and Computational Mathematics, 1033–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_285.

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Abdulle, Assyr. "Numerical Homogenization." In Encyclopedia of Applied and Computational Mathematics, 1066–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_394.

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Lee, S. L., W. A. M. Alwis, S. Swaddiwudhipong, and B. Mairantz. "Computational Aspect of Dynamic Analysis of Elastoplastic Arches." In Numerical Mathematics Singapore 1988, 285–94. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-6303-2_23.

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Тези доповідей конференцій з теми "Numerical and computational mathematics"

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Hundur, Yakup. "Preface of the "Symposium on computational nanomaterials"." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756530.

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Anandan, Princia, Florinda Schembri, and Maide Bucolo. "Computational modeling of droplet based logic circuits." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756102.

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Eoyang, Glenda H. "Human systems dynamics: Toward a computational model." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756214.

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Mateus, Artur, Geoffrey Mitchell, and Paulo Bártolo. "Computational fluid dynamics of reaction injection moulding." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756467.

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Kočí, Václav, Jiří Maděra, Miloš Jerman, Anton Trník, and Robert Černý. "Computational analysis of a modified guarded hot plate experiment." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756590.

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El Dabaghi, F., Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Review of a Common Computational Approach Combining Characteristics Methods and Mixed Finite Elements Formulations." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790092.

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Wang, Ruomei, Yi Li, Xiaonan Luo, Pingchang Zhang, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "The Numerical Simulation Computational Model of Dynamic Heat and Moisture Transfer in Fibrous Insulation." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790213.

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Hu, Jiankun, and Frank Jiang. "Preface of the “Workshop on computational intelligence and cyber security”." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756447.

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"European Society of Computational Methods in Sciences, Engineering and Technology (ESCMSET)." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756048.

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Mainzer, Klaus. "The cause of complexity in nature: An analytical and computational approach." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756213.

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Звіти організацій з теми "Numerical and computational mathematics"

1

French, Donald A. Numerical Analysis and Computation of Nonlinear Partial Differential Equations from Applied Mathematics. Fort Belvoir, VA: Defense Technical Information Center, November 1993. http://dx.doi.org/10.21236/ada275582.

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2

French, Donald A. Numerical Analysis and Computation of Nonlinear Partial Differential Equations from Applied Mathematics. Fort Belvoir, VA: Defense Technical Information Center, October 1990. http://dx.doi.org/10.21236/ada231188.

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3

Boisvert, Ronald F. Applied and computational mathematics division:. Gaithersburg, MD: National Institute of Standards and Technology, 2011. http://dx.doi.org/10.6028/nist.ir.7762.

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4

Boisvert, Ronald F. Applied and computational mathematics division:. Gaithersburg, MD: National Institute of Standards and Technology, May 2019. http://dx.doi.org/10.6028/nist.ir.8251.

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Boisvert, Ronald F. Applied and Computational Mathematics Division:. Gaithersburg, MD: National Institute of Standards and Technology, April 2020. http://dx.doi.org/10.6028/nist.ir.8306.

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Boisvert, Ronald F. Applied and Computational Mathematics Division:. Gaithersburg, MD: National Institute of Standards and Technology, 2022. http://dx.doi.org/10.6028/nist.ir.8423.

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7

Lax, P., and M. Berger. Applied analysis/computational mathematics. Final report 1993. Office of Scientific and Technical Information (OSTI), December 1993. http://dx.doi.org/10.2172/10113926.

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Prokaznikova, E. N. The distance learning course «The computational mathematics». OFERNIO, December 2018. http://dx.doi.org/10.12731/ofernio.2018.23530.

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Hall, Charles A., and Thomas A. Porsching. Computational Fluid Dynamics at ICMA (Institute for Computational Mathematics and Applications). Fort Belvoir, VA: Defense Technical Information Center, October 1988. http://dx.doi.org/10.21236/ada204967.

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10

Zirilli, Francesco. Mathematics: Numerical Solution of Inverse Problems in Acoustics. Fort Belvoir, VA: Defense Technical Information Center, April 1992. http://dx.doi.org/10.21236/ada267402.

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