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Relevant bibliographies by topics / Approximation of solutions

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Academic literature on the topic 'Approximation of solutions'

Author: Grafiati

Published: 14 March 2023

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Journal articles on the topic "Approximation of solutions"

1

Migda, Janusz, and Malgorzata Migda. "Approximation of Solutions to Nonautonomous Difference Equations." Tatra Mountains Mathematical Publications 71, no. 1 (2018): 109–21. http://dx.doi.org/10.2478/tmmp-2018-0010.

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Abstract We study the asymptotic properties of solutions to nonautonomous difference equations of the form $${\Delta ^m}{x_n} = {a_n}f(n,{x_{\sigma (n)}}) + {b_n},\,\,f:N \times {\Bbb R} \to {\Bbb R},\,\,\sigma :{\Bbb N} \to {\Bbb N}$$ Using the iterated remainder operator and asymptotic difference pairs we establish some results concerning approximative solutions and approximations of solutions. Our approach allows us to control the degree of approximation.

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Duma, Adrian, and Cristian Vladimirescu. "Approximation structures and applications to evolution equations." Abstract and Applied Analysis 2003, no. 12 (2003): 685–96. http://dx.doi.org/10.1155/s1085337503301010.

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We discuss various properties of the nonlinearA-proper operators as well as a generalized Leray-Schauder principle. Also, a method of approximating arbitrary continuous operators byA-proper mappings is described. We construct, via appropriate Browder-Petryshyn approximation schemes, approximative solutions for linear evolution equations in Banach spaces.

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Salas, Alvaro H., Wedad Albalawi, M. R. Alharthi, and S. A. El-Tantawy. "Some Novel Solutions to a Quadratically Damped Pendulum Oscillator: Analytical and Numerical Approximations." Complexity 2022 (May 28, 2022): 1–14. http://dx.doi.org/10.1155/2022/7803798.

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In this paper, some novel analytical and numerical techniques are introduced for solving and analyzing nonlinear second-order ordinary differential equations (ODEs) that are associated to some strongly nonlinear oscillators such as a quadratically damped pendulum equation. Two different analytical approximations are obtained: for the first approximation, the ansatz method with the help of Chebyshev approximate polynomial is employed to derive an approximation in the form of trigonometric functions. For the second analytical approximation, a novel hybrid homotopy with Krylov–Bogoliubov–Mitropol

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Kuzmina, E. V. "Generalized solutions of the Riccati equation." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 58, no. 2 (2022): 144–54. http://dx.doi.org/10.29235/1561-2430-2022-58-2-144-154.

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In this paper, we consider a nonlinear differential equation of the first order of the Riccati hierarchy. The concept of a generalized solution for such an equation cannot be introduced within the framework of the classical theory of generalized functions because the product of generalized functions is not defined. To introduce the concept of a generalized solution, two approaches are considered. In the first approach, approximation by solutions of the Cauchy problem with complex initial conditions is used, and generalized solutions are defined as limits of approximating families in the sense

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Stern, Steven. "Approximate Solutions to Stochastic Dynamic Programs." Econometric Theory 13, no. 3 (1997): 392–405. http://dx.doi.org/10.1017/s0266466600005867.

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This paper examines the properties of various approximation methods for solving stochastic dynamic programs in structural estimation problems. The problem addressed is evaluating the expected value of the maximum of available choices. The paper shows that approximating this by the maximum of expected values frequently has poor properties. It also shows that choosing a convenient distributional assumptions for the errors and then solving exactly conditional on the distributional assumption leads to small approximation errors even if the distribution is misspecified.

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Huang, Wentao, and Kechen Zhang. "Information-Theoretic Bounds and Approximations in Neural Population Coding." Neural Computation 30, no. 4 (2018): 885–944. http://dx.doi.org/10.1162/neco_a_01056.

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While Shannon's mutual information has widespread applications in many disciplines, for practical applications it is often difficult to calculate its value accurately for high-dimensional variables because of the curse of dimensionality. This article focuses on effective approximation methods for evaluating mutual information in the context of neural population coding. For large but finite neural populations, we derive several information-theoretic asymptotic bounds and approximation formulas that remain valid in high-dimensional spaces. We prove that optimizing the population density distribu

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Stanojević, Bogdana, and Milan Stanojević. "A computationally efficient algorithm to approximate the pareto front of multi-objective linear fractional programming problem." RAIRO - Operations Research 53, no. 4 (2019): 1229–44. http://dx.doi.org/10.1051/ro/2018083.

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The main contribution of this paper is the procedure that constructs a good approximation to the non-dominated set of multiple objective linear fractional programming problem using the solutions to certain linear optimization problems. In our approach we propose a way to generate a discrete set of feasible solutions that are further used as starting points in any procedure for deriving efficient solutions. The efficient solutions are mapped into non-dominated points that form a 0th order approximation of the Pareto front. We report the computational results obtained by solving random generated

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Lanzara, F., V. Maz'ya, and G. Schmidt. "Approximation of solutions to multidimensional parabolic equations by approximate approximations." Applied and Computational Harmonic Analysis 41, no. 3 (2016): 749–67. http://dx.doi.org/10.1016/j.acha.2015.06.001.

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Ganji, S. S., M. G. Sfahani, S. M. Modares Tonekaboni, A. K. Moosavi, and D. D. Ganji. "Higher-Order Solutions of Coupled Systems Using the Parameter Expansion Method." Mathematical Problems in Engineering 2009 (2009): 1–20. http://dx.doi.org/10.1155/2009/327462.

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We consider periodic solution for coupled systems of mass-spring. Three practical cases of these systems are explained and introduced. An analytical technique called Parameter Expansion Method (PEM) was applied to calculate approximations to the achieved nonlinear differential oscillation equations. Comparing with exact solutions, the first approximation to the frequency of oscillation produces tolerable error 3.14% as the maximum. By the second iteration the respective error became 1/5th, as it is 0.064%. So we conclude that the first approximation of PEM is so benefit when a quick answer is

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Crandall, S. H., and A. EI-Shafei. "Momentum and Energy Approximations for Elementary Squeeze-Film Damper Flows." Journal of Applied Mechanics 60, no. 3 (1993): 728–36. http://dx.doi.org/10.1115/1.2900865.

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To provide understanding of the effects of inertia on squeeze-film damper performance, two elementary flow patterns are studied. These elementary flows each depend on a single generalized motion coordinate whereas general planar motions of a damper are described by two independent generalized coordinates. Momentum and energy approximations for the elementary flows are compared with exact solutions. It is shown that the energy approximation, not previously applied to squeeze films, is superior to the momentum approximation in that at low Reynolds number the energy approximations agree with the

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Dissertations / Theses on the topic "Approximation of solutions"

1

Morini, Massimiliano. "Free-discontinuity problems: calibration and approximation of solutions." Doctoral thesis, SISSA, 2001. http://hdl.handle.net/20.500.11767/3923.

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Tarkhanov, Nikolai. "Unitary solutions of partial differential equations." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/2985/.

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Khan, Rahmat Ali. "Existence and approximation of solutions of nonlinear boundary value problems." Thesis, University of Glasgow, 2005. http://theses.gla.ac.uk/4037/.

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In chapter two, we establish new results for periodic solutions of some second order non-linear boundary value problems. We develop the upper and lower solutions method to show existence of solutions in the closed set defined by the well ordered lower and upper solutions. We develop the method of quasilinearization to approximate our problem by a sequence of solutions of linear problems that converges to the solution of the original problem quadratically. Finally, to show the applicability of our technique, we apply the theoretical results to a medical problem namely, a biomathematical model o

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Chidume, Chukwudi Soares de Souza Geraldo. "Iteration methods for approximation of solutions of nonlinear equations in Banach spaces." Auburn, Ala., 2008. http://repo.lib.auburn.edu/EtdRoot/2008/SUMMER/Mathematics_and_Statistics/Dissertation/Chidume_Chukwudi_33.pdf.

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Rouy, Elisabeth. "Approximation numérique des solutions de viscosité des équations d'Hamilton-Jacobi et exemple." Paris 9, 1992. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=1992PA090010.

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Cette thèse concerne l'approximation numérique des solutions de viscosité, telles qu'elles ont été définies par Michael Grain Crandall et Pierre-Louis Lions, des équations Hamilton-Jacobi du premier ordre qui sont des équations aux dérivées partielles non linéaires, ainsi que l'étude d'un exemple issu du traitement d'images, le shape-from-shading, qui consiste en la reconstruction d'un relief à trois dimensions à partir de la donnée d'une image en deux dimensions, d'une photographie par exemple. Le premier chapitre est une présentation succincte des solutions de viscosité des équations d’Hamil

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Badra, Mehdi. "Stabilisation par feedback et approximation des équations de Navier-Stokes." Toulouse 3, 2006. http://www.theses.fr/2006TOU30242.

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Cette thèse est consacrée à l'étude de problèmes de stabilisation par retour d'état ou "feedback" des équations de Navier-Stokes autour d'une solution stationnaire instable. Les cas d'un contrôle correspondant à une force exercée dans une partie du domaine et celui d'un contrôle localisé sur la frontière du domaine sont considérés. Le contrôle s'exprime en fonction du champ de vitesse à l'aide d'une loi de feedback linéaire. Celle-ci est fournie par la solution d'une équation de Riccati algébrique, dont la dérivation fait appel à la théorie du contrôle optimal. La question de l'approximation d

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Hugot, Hadrien. "Approximation et énumération des solutions efficaces dans les problèmes d'optimisation combinatoire multi-objectif." Paris 9, 2007. https://portail.bu.dauphine.fr/fileviewer/index.php?doc=2007PA090028.

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Cette thèse porte sur la résolution de problèmes d'optimisation combinatoire multi-objectif. La résolution de ces problèmes passe par la détermination de l'ensemble des solutions efficaces. Cependant, il peut s'avérer que le nombre de solutions efficaces soit très grand. Approcher l'ensemble des solutions efficaces d'un tel problème constitue, dès lors, un sujet de recherche central dans ce domaine. Les approches existantes sont souvent basées sur des méthodes approchées, de type (méta-)heuristiques, donc sans garantie sur la qualité des solutions trouvées. Des algorithmes d'approximation (à g

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Milišić, Vuk. "Approximation cinétique discrète de problèmes de lois de conservation avec bord." Bordeaux 1, 2001. http://www.theses.fr/2001BOR12449.

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Nous étudions l'approximation cinétique discrète de lois de conservation scalaires quasi-linéaires dans le quart d'espace positif. Cette approximation est obtenue par l'introduction de systèmes de type BGK relaxant la loi scalaire. Nous démontrons la convergence des systèmes semi-linéaires vers la loi scalaire. Nous discrétisons ces modèles pour obtenir une gamme de schémas numériques adaptés au problème avec bord. Dans une troisième partie, nous appliquons ces schémas à un certain nombre de cas test numériques.

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Bouhar, Mustapha. "Comportement limite de solutions d'équations quasi-linéaires dans des cylindres infinis." Tours, 1991. http://www.theses.fr/1991TOUR4002.

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On étudie le comportement asymptotique des solutions d'équations elliptiques quasi-linéaires avec un potentiel singulier dans un domaine au voisinage de zéro, au voisinage de l'infini du plan. L'étude de cette équation nous permet d'obtenir un certain nombre de configurations semblables à celles obtenues pour les solutions positives de la même équation sans potentiel dans un domaine borné et ouvert en dimension supérieure par P. L. Lions et Richard-Veron pour le cas sous-critique, P. Avilés pour le cas critique et Gidas-Spruck pour le cas sur-critique et dans le cas radial par M. F. Bidaut-Ver

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Yevik, Andrei. "Numerical approximations to the stationary solutions of stochastic differential equations." Thesis, Loughborough University, 2011. https://dspace.lboro.ac.uk/2134/7777.

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This thesis investigates the possibility of approximating stationary solutions of stochastic differential equations using numerical methods. We consider a particular class of stochastic differential equations, which are known to generate random dynamical systems. The existence of stochastic stationary solution is proved using global attractor approach. Euler's numerical method, applied to the stochastic differential equation, is proved to generate a discrete random dynamical system. The existence of stationary solution is proved again using global attractor approach. At last we prove that the

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Books on the topic "Approximation of solutions"

1

service), SpringerLink (Online, ed. Algebraic Approximation: A Guide to Past and Current Solutions. Springer Basel AG, 2012.

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Funaro, Daniele. Polynomial approximation of differential equations. Springer-Verlag, 1992.

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Bent, Fuglede, North Atlantic Treaty Organization. Scientific Affairs Division., and NATO Advanced Research Workshop on Approximation by Solutions of Partial Differential Equations, Quadrature Formulae, and Related Topics (1991 : Hanstholm, Denmark), eds. Approximation by solutions of partial differential equations. Kluwer Academic Publishers, 1992.

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Fuglede, B., M. Goldstein, W. Haussmann, W. K. Hayman, and L. Rogge, eds. Approximation by Solutions of Partial Differential Equations. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2436-2.

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Polynomial approximation of differential equations. Springer-Verlag, 1992.

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Quarteroni, Alfio. Numerical approximation of partial differential equations. 2nd ed. Springer, 1997.

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1953-, Valli A., ed. Numerical approximation of partial differential equations. Springer-Verlag, 1994.

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1946-, Chen Zhongying, and Chen G, eds. Approximate solutions of operator equations. World Scientific, 1997.

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Burstein, Joseph. Approximation by exponentials, their extensions & differential equations. Metrics Press, 1997.

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Křížek, M. Finite element approximation of variational problems and applications. Longman Scientific & Technical, 1990.

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Book chapters on the topic "Approximation of solutions"

1

Gauthier, P. M., J. Heinonen, and D. Zwick. "Axiomatic Approximation." In Approximation by Solutions of Partial Differential Equations. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2436-2_8.

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Tarkhanov, Nikolai N. "Uniform Approximation." In The Analysis of Solutions of Elliptic Equations. Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8804-1_5.

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Tarkhanov, Nikolai N. "Mean Approximation." In The Analysis of Solutions of Elliptic Equations. Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8804-1_6.

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Tarkhanov, Nikolai N. "BMO Approximation." In The Analysis of Solutions of Elliptic Equations. Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-015-8804-1_7.

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Shakarchi, Rami. "Approximation with Convolutions." In Problems and Solutions for Undergraduate Analysis. Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1738-1_12.

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Deutsch, Frank. "Generalized Solutions of Linear Equations." In Best Approximation in Inner Product Spaces. Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4684-9298-9_8.

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Sun, Shu-Ming, Ning Zhong, and Martin Ziegler. "Computability of the Solutions to Navier-Stokes Equations via Effective Approximation." In Complexity and Approximation. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-41672-0_7.

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Bardi, Martino, and Italo Capuzzo-Dolcetta. "Approximation and perturbation problems." In Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-0-8176-4755-1_6.

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Frontini, M., G. Rodriguez, and S. Seatzu. "An algorithm for computing minimum norm solutions of finite moment problem." In Algorithms for Approximation II. Springer US, 1990. http://dx.doi.org/10.1007/978-1-4899-3442-0_31.

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Bagby, T., and P. M. Gauthier. "Uniform Approximation by Global Harmonic Functions." In Approximation by Solutions of Partial Differential Equations. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2436-2_3.

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Conference papers on the topic "Approximation of solutions"

1

van der Herten, Joachim, Dirk Deschrijver, and Tom Dhaene. "Fuzzy local linear approximation-based sequential design." In 2014 IEEE Symposium on Computational Intelligence for Engineering Solutions (CIES). IEEE, 2014. http://dx.doi.org/10.1109/cies.2014.7011825.

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Elizalde-Blancas, Francisco, and Ismail B. Celik. "On the Representation of Numerical Solutions Using Taylor Series Approximation." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-31247.

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In this study, the representation of discretization error using Taylor series in finite difference solutions is investigated as well as the behavior of the exact solutions to the finite difference equations as a function of the grid size and grid refinement factor. The results are compared to the classical Richardson Extrapolation method whereby the numerical solution (or the error) is explicitly expressed as a Taylor series expansion. The exact finite difference solutions are used to demonstrate that oscillatory convergence is a common occurrence. The expansion of the numerical solutions in T

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Peng, Ya-Xin, Xi-Yan Hu, and Lei Zhang. "An Iterative Method for Bisymmetric Solutions and Optimal Approximation Solution of AXB=C." In Third International Conference on Natural Computation (ICNC 2007). IEEE, 2007. http://dx.doi.org/10.1109/icnc.2007.231.

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El-Shafei, A. "Modeling Finite Squeeze Film Dampers." In ASME Turbo Expo 2002: Power for Land, Sea, and Air. ASMEDC, 2002. http://dx.doi.org/10.1115/gt2002-30637.

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Most closed form solutions of Reynolds’ equation assume either a short bearing approximation or a long bearing approximation. These closed form approximations are used in rotordynamic simulation applications, otherwise a Finite Difference solution of Reynolds’ equation would be prohibitively time consuming. Recently, there have been proposed series solutions for Reynolds’ equation for special cases. In this paper, a perturbation solution to the governing equations is proposed to obtain a closed form solution of Reynolds’ equation for a finite squeeze film damper executing a circular centered o

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Jank, Gerhard, and Gábor Kun. "Solutions of generalized Riccati differential equations and their approximation." In Third CMFT Conference. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789812833044_0022.

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Dobkevich, Mariya, Felix Sadyrbaev, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Types of solutions and approximation of solutions of second order nonlinear boundary value problems." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241443.

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Allphin, Devin, and Joshua Hamel. "A Parallel Offline CFD and Closed-Form Approximation Strategy for Computationally Efficient Analysis of Complex Fluid Flows." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-38691.

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Computational fluid dynamics (CFD) solution approximations for complex fluid flow problems have become a common and powerful engineering analysis technique. These tools, though qualitatively useful, remain limited in practice by their underlying inverse relationship between simulation accuracy and overall computational expense. While a great volume of research has focused on remedying these issues inherent to CFD, one traditionally overlooked area of resource reduction for engineering analysis concerns the basic definition and determination of functional relationships for the studied fluid flo

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Djeridane, Badis, and John Lygeros. "Neural approximation of PDE solutions: An application to reachability computations." In Proceedings of the 45th IEEE Conference on Decision and Control. IEEE, 2006. http://dx.doi.org/10.1109/cdc.2006.377184.

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Bergmann, Ronny, and Dennis Merkert. "Approximation of periodic PDE solutions with anisotropic translation invariant spaces." In 2017 International Conference on Sampling Theory and Applications (SampTA). IEEE, 2017. http://dx.doi.org/10.1109/sampta.2017.8024347.

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Dong, Liang. "Analytical solutions for nonlinear waveguide equation under Gaussian mode approximation." In Lasers and Applications in Science and Engineering, edited by Jes Broeng and Clifford Headley III. SPIE, 2008. http://dx.doi.org/10.1117/12.774052.

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Reports on the topic "Approximation of solutions"

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Herzog, K. J., M. D. Morris, and T. J. Mitchell. Bayesian approximation of solutions to linear ordinary differential equations. Office of Scientific and Technical Information (OSTI), 1990. http://dx.doi.org/10.2172/6242347.

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Kamai, Tamir, Gerard Kluitenberg, and Alon Ben-Gal. Development of heat-pulse sensors for measuring fluxes of water and solutes under the root zone. United States Department of Agriculture, 2016. http://dx.doi.org/10.32747/2016.7604288.bard.

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The objectives defined for this study were to: (1) develop a heat-pulse sensor and a heat-transfer model for leaching measurement, and (2) conduct laboratory study of the sensor and the methodology to estimate leaching flux. In this study we investigated the feasibility for estimating leachate fluxes with a newly designed heat-pulse (HP) sensor, combining water flux density (WFD) with electrical conductivity (EC) measurements in the same sensor. Whereas previous studies used the conventional heat pulse sensor for these measurements, the focus here was to estimate WFD with a robust sensor, appr

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Hart, Carl, and Gregory Lyons. A tutorial on the rapid distortion theory model for unidirectional, plane shearing of homogeneous turbulence. Engineer Research and Development Center (U.S.), 2022. http://dx.doi.org/10.21079/11681/44766.

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The theory of near-surface atmospheric wind noise is largely predicated on assuming turbulence is homogeneous and isotropic. For high turbulent wavenumbers, this is a fairly reasonable approximation, though it can introduce non-negligible errors in shear flows. Recent near-surface measurements of atmospheric turbulence suggest that anisotropic turbulence can be adequately modeled by rapid-distortion theory (RDT), which can serve as a natural extension of wind noise theory. Here, a solution for the RDT equations of unidirectional plane shearing of homogeneous turbulence is reproduced. It is ass

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Gilsinn, David E. Approximating periodic solutions of autonomous delay differential equations. National Institute of Standards and Technology, 2006. http://dx.doi.org/10.6028/nist.ir.7375.

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Campbell, Stephen L. Distributional Convergence of BDF (Backward Differentiation Formulas) Approximations to Solutions of Descriptor Systems. Defense Technical Information Center, 1987. http://dx.doi.org/10.21236/ada190819.

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Eggertsson, Gauti, and Sanjay Singh. Log-linear Approximation versus an Exact Solution at the ZLB in the New Keynesian Model. National Bureau of Economic Research, 2016. http://dx.doi.org/10.3386/w22784.

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Domich, P. D. A near-optimal starting solution for polynomial approximation of a continuous function in the L₁ norm. National Bureau of Standards, 1986. http://dx.doi.org/10.6028/nbs.ir.86-3389.

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Rojas-Bernal, Alejandro, and Mauricio Villamizar-Villegas. Pricing the exotic: Path-dependent American options with stochastic barriers. Banco de la República de Colombia, 2021. http://dx.doi.org/10.32468/be.1156.

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We develop a novel pricing strategy that approximates the value of an American option with exotic features through a portfolio of European options with different maturities. Among our findings, we show that: (i) our model is numerically robust in pricing plain vanilla American options; (ii) the model matches observed bids and premiums of multidimensional options that integrate Ratchet, Asian, and Barrier characteristics; and (iii) our closed-form approximation allows for an analytical solution of the option’s greeks, which characterize the sensitivity to various risk factors. Finally, we highl

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Tal-Ezer, Hillel. Polynominal Approximation of Functions of Matrices and Its Application the the Solution of a General System of Linear Equations. Defense Technical Information Center, 1987. http://dx.doi.org/10.21236/ada211390.

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Trenchea, Catalin. Efficient Numerical Approximations of Tracking Statistical Quantities of Interest From the Solution of High-Dimensional Stochastic Partial Differential Equations. Defense Technical Information Center, 2012. http://dx.doi.org/10.21236/ada567709.

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