Relevant bibliographies by topics / Rigorous numerical methods

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Rigorous numerical methods'

Author: Grafiati
Published: 24 April 2022

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Journal articles on the topic "Rigorous numerical methods"

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Church, Kevin E. M., and Clément Fortin. "Computer-Assisted Methods for Analyzing Periodic Orbits in Vibrating Gravitational Billiards." International Journal of Bifurcation and Chaos 31, no. 08 (2021): 2130021. http://dx.doi.org/10.1142/s0218127421300214.

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Using rigorous numerical methods, we prove the existence of 608 isolated periodic orbits in a gravitational billiard in a vibrating unbounded parabolic domain. We then perform pseudo-arclength continuation in the amplitude of the parabolic surface’s oscillation to compute large, global branches of periodic orbits. These branches are themselves proven rigorously using computer-assisted methods. Our numerical investigations strongly suggest the existence of multiple pitchfork bifurcations in the billiard model. Based on the numerics, physical intuition and existing results for a simplified model
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Schmitz, M., R. Bräuer, and O. Bryngdahl. "Comment on numerical stability of rigorous differential methods of diffraction." Optics Communications 124, no. 1-2 (1996): 1–8. http://dx.doi.org/10.1016/0030-4018(95)00674-5.

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Kelly, David, Andrew J. Majda, and Xin T. Tong. "Concrete ensemble Kalman filters with rigorous catastrophic filter divergence." Proceedings of the National Academy of Sciences 112, no. 34 (2015): 10589–94. http://dx.doi.org/10.1073/pnas.1511063112.

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The ensemble Kalman filter and ensemble square root filters are data assimilation methods used to combine high-dimensional, nonlinear dynamical models with observed data. Ensemble methods are indispensable tools in science and engineering and have enjoyed great success in geophysical sciences, because they allow for computationally cheap low-ensemble-state approximation for extremely high-dimensional turbulent forecast models. From a theoretical perspective, the dynamical properties of these methods are poorly understood. One of the central mysteries is the numerical phenomenon known as catast
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Ayres, José Eduardo de Almeida, and Luiz Henrique de Figueiredo. "Interval Methods for Fixed and Periodic Points: Development and Visualization." JUCS - Journal of Universal Computer Science 26, no. 10 (2020): 1312–30. http://dx.doi.org/10.3897/jucs.2020.068.

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We describe the development of rigorous numerical methods based on interval analysis for finding all fixed points of a map and all attracting periodic points of a complex polynomial. We also discuss their performance with instructive visualizations.
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Yang, Yin, Yanping Chen, Yunqing Huang, and Wei Yang. "Convergence Analysis of Legendre-Collocation Methods for Nonlinear Volterra Type Integro Equations." Advances in Applied Mathematics and Mechanics 7, no. 1 (2015): 74–88. http://dx.doi.org/10.4208/aamm.2013.m163.

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AbstractA Legendre-collocation method is proposed to solve the nonlinear Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicate that the numerical errors inL2-norm andL∞-norm will decay exponentially provided that the kernel function is sufficiently smooth. Numerical results are presented, which confirm the theoretical prediction of the exponential rate of convergence.
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Meeks, Crawford R., and Long Tran. "Ball Bearing Dynamic Analysis Using Computer Methods—Part I: Analysis." Journal of Tribology 118, no. 1 (1996): 52–58. http://dx.doi.org/10.1115/1.2837092.

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An analytical ball bearing dynamics model was developed that rigorously models all of the significant kinematic, structural, and dynamic effects. The model can analyze bearings of any material combination for the races, balls and ball cage. This model analyzes the stresses and deflections of the loaded elements due to (1) preload, (2) external axial, radial and moment loads, (3) centrifugal and gyroscopic ball loads. A rigorous six-degree-of-freedom model of ball cage motions was developed to analyze ball and cage dynamics. The ball cage equations of motion were written in a rotating coordinat
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Yang, Yin, and Yunqing Huang. "Spectral-Collocation Methods for Fractional Pantograph Delay-Integrodifferential Equations." Advances in Mathematical Physics 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/821327.

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We propose and analyze a spectral Jacobi-collocation approximation for fractional order integrodifferential equations of Volterra type with pantograph delay. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis for the collocation method, which shows that the error of approximate solution decays exponentially inL∞norm and weightedL2-norm. The numerical examples are given to illustrate the theoretical results.
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Fairuzov, Yuri V., and Hector Arvizu. "Numerical Solution for Transient Conjugate Two-Phase Heat Transfer With Heat Generation in the Pipe Wall." Journal of Heat Transfer 124, no. 6 (2002): 1213–18. http://dx.doi.org/10.1115/1.1470170.

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A method developed earlier for modeling conjugate two-phase heat transfer in flashing flows was used to obtain a numerical solution for transient boiling flow in heated pipes or channels. Two criteria of applicability of the solution obtained were proposed and numerically tested using a more rigorous model, which accounts for the effects of heat conduction with heat generation in the wall and forced convective boiling. The solution obtained provides a simple and reliable alternative to more rigorous methods for modeling transient two-phase flow in heated channels when the material of the wall
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HEWETT, D. P. "Shadow boundary effects in hybrid numerical-asymptotic methods for high-frequency scattering." European Journal of Applied Mathematics 26, no. 5 (2015): 773–93. http://dx.doi.org/10.1017/s0956792515000315.

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The hybrid numerical-asymptotic (HNA) approach aims to reduce the computational cost of conventional numerical methods for high-frequency wave scattering problems by enriching the numerical approximation space with oscillatory basis functions, chosen based on partial knowledge of the high-frequency solution asymptotics. In this paper, we propose a new methodology for the treatment of shadow boundary effects in HNA boundary element methods, using the classical geometrical theory of diffraction phase functions combined with mesh refinement. We develop our methodology in the context of scattering
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Aldosary, Muhannad, Jinsheng Wang, and Chenfeng Li. "Structural reliability and stochastic finite element methods." Engineering Computations 35, no. 6 (2018): 2165–214. http://dx.doi.org/10.1108/ec-04-2018-0157.

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Purpose This paper aims to provide a comprehensive review of uncertainty quantification methods supported by evidence-based comparison studies. Uncertainties are widely encountered in engineering practice, arising from such diverse sources as heterogeneity of materials, variability in measurement, lack of data and ambiguity in knowledge. Academia and industries have long been researching for uncertainty quantification (UQ) methods to quantitatively account for the effects of various input uncertainties on the system response. Despite the rich literature of relevant research, UQ is not an easy
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Dissertations / Theses on the topic "Rigorous numerical methods"

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Iff, Wolfgang [Verfasser], and Norbert [Akademischer Betreuer] Lindlein. "Rigorous Fourier Methods Based on Numerical Integration for the Calculation of Diffractive Optical Systems / Wolfgang Iff. Gutachter: Norbert Lindlein." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2016. http://d-nb.info/108212916X/34.

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Day, Sarah. "A rigorous numerical method in infinite dimensions." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/28983.

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Thiam, Abdoulaye. "A rigorous numerical method for the proof of Galaktionov-Svirshchevskii's conjecture." Master's thesis, Université Laval, 2016. http://hdl.handle.net/20.500.11794/26595.

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La théorie des systèmes dynamiques étudie les phénomènes qui évoluent au cours du temps. Plus précisément, un système dynamique est donné par : un espace de phase dont les points correspondent à des états possibles du système étudié et une loi d'évolution décrivant l'infinitésimal (pour le cas continu) pas à pas (pour le cas discret) les changements des états du système. Le but de la théorie est de comprendre l'évolution dans le long terme. Dans ce travail, nous présentons une nouvelle méthode pour la résolution des systèmes linéaires avec preuve assistée par ordinateur dans le cadre de modèle
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Kuhn, Wolfgang. "Rigorous and reasonable error bounds for the numerical solution of dynamical systems." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/28941.

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Mascherpa, Fabio [Verfasser]. "A new quantitative approach to general bosonic environments in open quantum systems : rigorous error bounds and a novel numerical method for finite systems / Fabio Mascherpa." Ulm : Universität Ulm, 2019. http://d-nb.info/119504836X/34.

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Joldes, Mioara Maria. "Approximations polynomiales rigoureuses et applications." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2011. http://tel.archives-ouvertes.fr/tel-00657843.

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Quand on veut évaluer ou manipuler une fonction mathématique f, il est fréquent de la remplacer par une approximation polynomiale p. On le fait, par exemple, pour implanter des fonctions élémentaires en machine, pour la quadrature ou la résolution d'équations différentielles ordinaires (ODE). De nombreuses méthodes numériques existent pour l'ensemble de ces questions et nous nous proposons de les aborder dans le cadre du calcul rigoureux, au sein duquel on exige des garanties sur la précision des résultats, tant pour l'erreur de méthode que l'erreur d'arrondi.Une approximation polynomiale rigo
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Bréhard, Florent. "Certified numerics in function spaces : polynomial approximations meet computer algebra and formal proof." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSEN032/document.

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Le calcul rigoureux vise à produire des représentations certifiées pour les solutions de nombreux problèmes, notamment en analyse fonctionnelle, comme des équations différentielles ou des problèmes de contrôle optimal. En effet, certains domaines particuliers comme l’ingénierie des systèmes critiques ou les preuves mathématiques assistées par ordinateur ont des exigences de fiabilité supérieures à ce qui peut résulter de l’utilisation d’algorithmes relevant de l’analyse numérique classique.Notre objectif consiste à développer des algorithmes à la fois efficaces et validés / certifiés, dans le
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Szczelina, Robert. "Rigorous integration of Delay Differential Equations." Praca doktorska, 2015. http://ruj.uj.edu.pl/xmlui/handle/item/42188.

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Walawska, Irmina. "Algorytmy ścisłego całkowania równań wariacyjnych i ich zastosowania do badania bifurkacji rozwiązań okresowych w Kołowym Ograniczonym Problemie Trzech Ciał." Praca doktorska, 2019. https://ruj.uj.edu.pl/xmlui/handle/item/77178.

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Pałka, Wiesław. "Rigorous numerical analysis with a finite element method." Praca doktorska, 2014. https://ruj.uj.edu.pl/xmlui/handle/item/58207.

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W przedkładanej rozprawie, dla wysoko wymiarowej dyskretyzacji równania Burgersa, zostaje przedstawiony komputerowo wspierany dowód istnienia orbity okresowej. Główny wynik został uzyskany poprzez połączenie Metody Elementów Skończonych z techniką nazywającą się self-consistent bounds. Najpierw tworzona jest skończenie wymiarowa inkluzja różniczkowa, która zawiera rozwiązanie równania różniczkowego cząstkowego, a następnie jest ona rozwiązywana przy pomocy ścisłych obliczeń numerycznych.<br>This thesis is devoted to the computer assisted proof of the existence of periodic orbit for a high dime
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Books on the topic "Rigorous numerical methods"

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Coolen, Ton, Alessia Annibale, and Ekaterina Roberts. Generating Random Networks and Graphs. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.001.0001.

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This book supports researchers who need to generate random networks, or who are interested in the theoretical study of random graphs. The coverage includes exponential random graphs (where the targeted probability of each network appearing in the ensemble is specified), growth algorithms (i.e. preferential attachment and the stub-joining configuration model), special constructions (e.g. geometric graphs and Watts Strogatz models) and graphs on structured spaces (e.g. multiplex networks). The presentation aims to be a complete starting point, including details of both theory and implementation,
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Book chapters on the topic "Rigorous numerical methods"

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Igreja, J. M. "Rigorous numerical method for irrigation canal system dynamics and control." In 2015 Proceedings of the Conference on Control and its Applications. Society for Industrial and Applied Mathematics, 2015. http://dx.doi.org/10.1137/1.9781611974072.14.

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Mrozek, M., and P. Pilarczyk. "The Conley Index and Rigorous Numerics for Attracting Periodic Orbits." In Variational and Topological Methods in the Study of Nonlinear Phenomena. Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0081-9_5.

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Hartmann, Stefan, and Steffen Rothe. "A Rigorous Application of the Method of Vertical Lines to Coupled Systems in Finite Element Analysis." In Notes on Numerical Fluid Mechanics and Multidisciplinary Design. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-33221-0_10.

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Figueras, Jordi-Lluís, and Àlex Haro. "The Parameterization Method for Quasi-Periodic Systems: From Rigorous Results to Validated Numerics." In Applied Mathematical Sciences. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-29662-3_3.

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"Numerical Methods for Rigorous Diffraction Theory." In Diffraction, Fourier Optics and Imaging. John Wiley & Sons, Inc., 2006. http://dx.doi.org/10.1002/9780470085004.ch20.

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Kunze, Markus. "Rigorous Methods and Numerical Results for Dry Friction Problems." In World Scientific Series on Nonlinear Science Series A. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812796301_0009.

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Roach, G. F., I. G. Stratis, and A. N. Yannacopoulos. "Well Posedness." In Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics. Princeton University Press, 2012. http://dx.doi.org/10.23943/princeton/9780691142173.003.0004.

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This chapter presents rigorous mathematical results concerning the solvability and well posedness of time-harmonic problems for complex electromagnetic media, with a special emphasis on chiral media. It also presents some results concerning eigenvalue problems in cavities filled with complex electromagnetic materials. The chapter also studies the behaviour of the interior domain problem for a chiral medium in the limit of low chirality. Next, it presents some comments related to the well posedness and solvability of exterior problems. Finally, using an appropriate finite-dimensional space and the variational formulation of the discretised version of the original boundary value problem, this chapter obtains numerical methods for the solution of the Maxwell equations for chiral media.
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Bažant, Zdeněk P., Jia-Liang Le, and Marco Salviato. "Fundamentals of Linear Elastic Fracture Mechanics." In Quasibrittle Fracture Mechanics and Size Effect. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192846242.003.0002.

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The linear elastic fracture mechanics (LEFM) is the pillar of all fracture mechanics. In this chapter, it is presented in full, with complete derivations and many examples. Griffith's concept of the energy release rates is described, the elastic singular near-tip stress field is derived, and the stress intensity factors are defined. Their relation to the energy release rate, discovered by Irwin, is derived, and three different fracture modes in isotropic solids are defined. A rigorous derivation of Rice's J-integral is given and illustrated by examples. Various ways of numerical calculation of the stress intensity factors are reviewed. It is shown how the elastic compliance and deflections due to a crack or a system of cracks under external loads or crack pressure can be calculated from the known stress intensity factors. Various LEFM methods of calculating and measuring the energy release rate and fracture energy are presented and test control by a crack-mouth or crack-tip gage is explained. The complex singularities at interfacial cracks are described. The remote decay of the stress field disturbance by a crack is also derived. The chapter ends with comments on anisotropic materials and on three-dimensional singularities at the intersection of crack edge with the surface.
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Valeriani, Manfredi, and Vicki L. Plano Clark. "Mixed Methods." In Research Methods in the Social Sciences: An A-Z of key concepts. Oxford University Press, 2021. http://dx.doi.org/10.1093/hepl/9780198850298.003.0041.

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This chapter examines mixed-methods research, which is an approach that involves the integration of quantitative and qualitative methods at one or more stages of a research study. The central idea behind mixed-methods research is that the intentional combination of numeric-based methods with narrative-based methods can best provide answers to some research questions. The ongoing attempts to construct a simple and common conceptualization of mixed-methods provide a good indicator of the status of mixed-methods itself. mixed-methods research has emerged as a formalized methodology well suited to addressing complex problems, and is currently applied throughout the social sciences and beyond. Nowadays, researchers interested in combining quantitative and qualitative methods can benefit from the growing knowledge about the epistemological foundations, essential considerations, and rigorous designs that have been advanced for mixed-methods research.
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Bulatov, Vasily, and Wei Cai. "Fundamentals of Atomistic Simulations." In Computer Simulations of Dislocations. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198526148.003.0006.

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Fundamentally, materials derive their properties from the interaction between their constituent atoms. These basic interactions make the atoms assemble in a particular crystalline structure. The same interactions also define how the atoms prefer to arrange themselves in the dislocation core. Therefore, to understand the behavior of dislocations, it is necessary and sufficient to study the collective behavior of atoms in crystals populated by dislocations. This chapter introduces the basic methodology of atomistic simulations that will be applied to the studies of dislocations in the following chapters. Section 1 discusses the nature of interatomic interactions and introduces empirical models that describe these interactions with various degrees of accuracy. Section 2 introduces the significance of the Boltzmann distribution that describes statistical properties of a collection of interacting atoms in thermal equilibrium. This section sets the stage for a subsequent discussion of basic computational methods to be used throughout this book. Section 3 covers the methods for energy minimization. Sections 4 and 5 give a concise introduction to Monte Carlo and molecular dynamics methods. When put close together, atoms interact by exerting forces on each other. Depending on the atomic species, some interatomic interactions are relatively easy to describe, while others can be very complicated. This variability stems from the quantum mechanical motion and interaction of electrons [15, 16]. Henceforth, rigorous treatment of interatomic interactions should be based on a solution of Schrödinger’s equation for interacting electrons, which is usually referred to as the first principles or ab initio theory. Numerical calculations based on first principles are computationally very expensive and can only deal with a relatively small number of atoms. In the context of dislocation modelling, relevant behaviors often involve many thousands of atoms and can only be approached using much less sophisticated but more computationally efficient models. Even though we do not use it in this book, it is useful to bear in mind that the first principles theory provides a useful starting point for constructing approximate but efficient models that are needed to study large-scale problems involving many atoms.
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Conference papers on the topic "Rigorous numerical methods"

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Duracz, Adam, Ferenc A. Bartha, and Walid Taha. "Accurate rigorous simulation should be possible for good designs." In 2016 International Workshop on Symbolic and Numerical Methods for Reachability Analysis (SNR). IEEE, 2016. http://dx.doi.org/10.1109/snr.2016.7479376.

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He, Lingfang, Haogang Wang, Xianmin Zhang, Xiaofeng Jin, and Huan Yu. "A study on the near field OAM using the rigorous numerical methods." In 2014 3rd Asia-Pacific Conference on Antennas and Propagation. IEEE, 2014. http://dx.doi.org/10.1109/apcap.2014.6992631.

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Qingquan, Pan, Lu Haoliang, Li Dongsheng, and Wang Kan. "The Rigorous SP3 Theory and Study on its Numerical Verification." In 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-67309.

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On the premise of no mathematical approximation, the rigorous SP3 theory which is deduced from the theoretical basis of the 3rd-order spherical harmonic method and the simplified harmonic method has more definite physical meaning. Compared with the conventional SP3 theory, the interface and boundary conditions of the rigorous SP3 theory are obtained according to the continuity of angular flux, and the angular flux is also established a relationship with each order scalar flux, which provides the theoretical solution to the discontinuous factors applied to the SP3 equation. However, the interfa
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Campana, Emilio F., Daniele Peri, Yusuke Tahara, Manivannan Kandasamy, and Frederick Stern. "Numerical Optimization Methods for Ship Hydrodynamic Design." In SNAME Maritime Convention. SNAME, 2009. http://dx.doi.org/10.5957/smc-2009-013.

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The use of computational methods in design engineering is growing rapidly at all stages of the design process, with the final goal of a substantial reduction of the cost and time for the development of a design. Simulations and optimization algorithms can be combined together into what is known as Simulation-Based Design (SBD) techniques. Using these tools the designers may find the minimum of some user defined objective functions with constraints, under the general mathematical framework of a Non-Linear Programming problem. There are problems of course: computational complexity, noise, robust
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Yonatan, Prigiarto Hokkal, Filip Van den Abeele, and Jean-Christophe Ballard. "Numerical Simulation of Upheaval Buckling Using “Intelligent” Backfill Soil Springs." In ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/omae2015-42141.

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Designing the cover height of buried pipelines to prevent them from buckling requires a method that can thoroughly and realistically model the phenomenon. This paper introduces a new technique to assess the risk of upheaval buckling (UHB) by using backfill soil springs (BFSS) to represent the uplift resistance provided by the backfill soil on top of a buried pipeline. This paper investigates the pre-buckling pipeline behavior related to UHB and highlights some of the key parameters governing the analysis. UHB assessment based on a case study was carried out and the results were then compared w
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Renson, L., and G. Kerschen. "Numerical Computation of Nonlinear Normal Modes of Nonconservative Systems." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12895.

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Since linear modal analysis fails in the presence of non-linear dynamical phenomena, the concept of nonlinear normal modes (NNMs) was introduced with the aim of providing a rigorous generalization of linear normal modes to nonlinear systems. Initially defined as periodic solutions, numerical techniques such as the continuation of periodic solutions were used to compute NNMs. Because these methods are limited to conservative systems, the present study targets the computation of NNMs for non-conservative systems. Their definition as invariant manifolds in phase space is considered. Specifically,
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Park, Gyuhae, Amanda C. Rutherford, Hoon Sohn, and Charles R. Farrar. "Damage Identification Using Impedance Methods Coupled With Statistical Classifiers." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-43179.

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This paper presents the use of statistically rigorous algorithms combined with active-sensing impedance methods for damage identification in engineering systems. In particular, we propose to use statistical pattern recognition methods to address damage classification and data mining issues associated with the examination of large numbers of impedance signals for health monitoring applications. The impedance-based structural health monitoring technique, which utilizes electromechanical coupling properties of piezoelectric materials, has shown feasibility for use in a variety of damage identific
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Rediniotis, Othon K., and Andrew J. Kurdila. "Reduced Order Nonlinear Navier Stokes Models for Synthetic Jets." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8065.

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Abstract While the potential for the use of synthetic jet actuators to achieve flow control has been noted fro some tme, most studies of these devices have been empirical or experimental in nature. Several technical issues must be resolved to achieve rigorous, model-based, closed loop control methodologies for this class of actuator. The goal of this paper is consequently two-fold. First, we seek to derive and evaluate model order reduction methods based on proper orthogonal decomposition that are suitable for synthetic jet actuators. Secondly, we seek to derive rigorously stable feedback cont
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Ageno, Alessio, and Anna Sinopoli. "Stability Analysis of the Rocking Block: Numerical Investigations on Analytical Stability Boundaries." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48478.

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The present paper illustrates some recently developed techniques to evaluate stability features, such as characteristic multipliers and Lyapunov’s exponents, for a problem with strong discontinuities. The problem analyzed concerns the plane dynamics of a rigid block simply supported on a harmonically moving rigid ground. In previous papers [1–3] many aspects have been investigated and the following results have been carried out: 1. the general procedure to approach numerically the problem has been outlined; 2. a rigorous method has been established to calculate characteristic multipliers and L
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Krueger, Aaron M., Vincent A. Mousseau, and Yassin A. Hassan. "Rigorous Code Verification: An Additional Tool to Use With the Method of Manufactured Solutions." In ASME 2019 Verification and Validation Symposium. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/vvs2019-5166.

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Abstract The Method of Manufactured Solutions (MMS) has proven to be useful for completing code verification studies. MMS allows the code developer to verify that the observed order-of-accuracy matches the theoretical order-of accuracy. Even though the solution to the partial differential equation is not intuitive, it provides an exact solution to a problem that most likely could not be solved analytically. The code developer can then use the exact solution as a debugging tool. While the order-of-accuracy test has been historically treated as the most rigorous of all code verification methods,
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Reports on the topic "Rigorous numerical methods"

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Russo, David, Daniel M. Tartakovsky, and Shlomo P. Neuman. Development of Predictive Tools for Contaminant Transport through Variably-Saturated Heterogeneous Composite Porous Formations. United States Department of Agriculture, 2012. http://dx.doi.org/10.32747/2012.7592658.bard.

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The vadose (unsaturated) zone forms a major hydrologic link between the ground surface and underlying aquifers. To understand properly its role in protecting groundwater from near surface sources of contamination, one must be able to analyze quantitatively water flow and contaminant transport in variably saturated subsurface environments that are highly heterogeneous, often consisting of multiple geologic units and/or high and/or low permeability inclusions. The specific objectives of this research were: (i) to develop efficient and accurate tools for probabilistic delineation of dominant geol
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