Relevant bibliographies by topics / Numerical error analysis

Contents

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

Academic literature on the topic 'Numerical error analysis'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 February 2022

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Journal articles on the topic "Numerical error analysis"

1

T., V., Solomon G. Mikhlin, and Reinhard Lehmann. "Error Analysis in Numerical Processes." Mathematics of Computation 60, no. 201 (1993): 431. http://dx.doi.org/10.2307/2153180.

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Faber, Vance, and Thomas A. Manteuffel. "Orthogonal Error Methods." SIAM Journal on Numerical Analysis 24, no. 1 (1987): 170–87. http://dx.doi.org/10.1137/0724014.

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Ditkowski, Adi, Sigal Gottlieb, and Zachary J. Grant. "Two-Derivative Error Inhibiting Schemes and Enhanced Error Inhibiting Schemes." SIAM Journal on Numerical Analysis 58, no. 6 (2020): 3197–225. http://dx.doi.org/10.1137/19m1306129.

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Cui, Jing Jun. "Analysis of Machining Error in Numerical Control Milling." Applied Mechanics and Materials 312 (February 2013): 710–13. http://dx.doi.org/10.4028/www.scientific.net/amm.312.710.

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Generally speaking, the error in machining is an important indicator measuring the accuracy of finished surface. The machining error often occurs in numerical control milling. Such error will be influenced by multiple factors, such as cutter wear, thermal deformation, machine tool deformation, vibration or positioning error. Nowadays, though our science and technology develops rapidly, machining error problem in numerical control milling occurs frequently. At present, several methods can be applied to forecast machining error problems in numerical control milling, including on the basis of machining theory, experimental study, design study and artificial intelligence. The analysis and forecast of machining error problems in numerical control milling can to some extent improve the degree of machining errors so as to promote the machining accuracy in milling. The author expresses the views on machining error problems according to current situations of numerical control milling.
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Kuperberg, Greg. "Numerical Cubature Using Error-Correcting Codes." SIAM Journal on Numerical Analysis 44, no. 3 (2006): 897–907. http://dx.doi.org/10.1137/040615572.

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Reich, Sebastian. "Backward Error Analysis for Numerical Integrators." SIAM Journal on Numerical Analysis 36, no. 5 (1999): 1549–70. http://dx.doi.org/10.1137/s0036142997329797.

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Connors, Jeffrey M., Jeffrey W. Banks, Jeffrey A. Hittinger, and Carol S. Woodward. "A Method to Calculate Numerical Errors Using Adjoint Error Estimation for Linear Advection." SIAM Journal on Numerical Analysis 51, no. 2 (2013): 894–926. http://dx.doi.org/10.1137/110845100.

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Wetton, Brian R. "Error Analysis of Pressure Increment Schemes." SIAM Journal on Numerical Analysis 38, no. 1 (2000): 160–69. http://dx.doi.org/10.1137/s0036142998338538.

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Axelsson, O., and L. Kolotilina. "Monotonicity and Discretization Error Estimates." SIAM Journal on Numerical Analysis 27, no. 6 (1990): 1591–611. http://dx.doi.org/10.1137/0727093.

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Aves, Mark A., David F. Griffiths, and Desmond J. Higham. "Does Error Control Suppress Spuriosity?" SIAM Journal on Numerical Analysis 34, no. 2 (1997): 756–78. http://dx.doi.org/10.1137/s0036142994276980.

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Dissertations / Theses on the topic "Numerical error analysis"

1

Romutis, Todd. "Numerical Smoothness and Error Analysis for Parabolic Equations." Bowling Green State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1522150799203255.

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Ndamase-, Nzuzo Pumla Patricia. "Numerical error analysis in foundation phase (Grade 3) mathematics." Thesis, University of Fort Hare, 2014. http://hdl.handle.net/10353/5893.

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The focus of the research was on numerical errors committed in foundation phase mathematics. It therefore explored: (1) numerical errors learners in foundation phase mathematics encounter (2) relationships underlying numerical errors and (3) the implementable strategies suitable for understanding numerical error analysis in foundation phase mathematics (Grade 3). From 375 learners who formed the population of the study in the primary schools (16 in total), the researcher selected by means of a simple random sample technique 80 learners as the sample size, which constituted 10% of the population as response rate. On the basis of the research questions and informed by positivist paradigm, a quantitative approach was used by means of tables, graphs and percentages to address the research questions. A Likert scale was used with four categories of responses ranging from (A) Agree, (S A) Strongly Agree, (D) Disagree and (S D) Strongly Disagree. The results revealed that: (1) the underlying numerical errors that learners encounter, include the inability to count backwards and forwards, number sequencing, mathematical signs, problem solving and word sums (2) there was a relationship between committing errors and a) copying numbers b) confusion of mathematical signs or operational signs c) reading numbers which contained more than one digit (3) It was also revealed that teachers needed frequent professional training for development; topics need to change and lastly government needs to involve teachers at ground roots level prior to policy changes on how to implement strategies with regards to numerical errors in the foundational phase. It is recommended that attention be paid to the use of language and word sums in order to improve cognition processes in foundation phase mathematics. Moreover, it recommends that learners are to be assisted time and again when reading or copying their work, so that they could have fewer errors in foundation phase mathematics. Additionally it recommends that teachers be trained on how to implement strategies of numerical error analysis in foundation phase mathematics. Furthermore, teachers can use tests to identify learners who could be at risk of developing mathematical difficulties in the foundation phase.
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Reddinger, Kaitlin Sue. "Numerical Stability & Numerical Smoothness of Ordinary Differential Equations." Bowling Green State University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1431597407.

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Pinchuk, Amy Ruth. "Automatic adaptive finite element mesh generation and error estimation." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=63269.

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Higham, D. J. "Error control in nonstiff initial value solvers." Thesis, University of Manchester, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234210.

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Balsubramanian, Ravishankar. "Error estimation and grid adaptation for functional outputs using discrete-adjoint sensitivity analysis." Master's thesis, Mississippi State : Mississippi State University, 2002. http://library.msstate.edu/etd/show.asp?etd=etd-10032002-113749.

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Shaw, Jeremy A. "Computational Algorithms for Improved Representation of the Model Error Covariance in Weak-Constraint 4D-Var." PDXScholar, 2017. https://pdxscholar.library.pdx.edu/open_access_etds/3473.

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Four-dimensional variational data assimilation (4D-Var) provides an estimate to the state of a dynamical system through the minimization of a cost functional that measures the distance to a prior state (background) estimate and observations over a time window. The analysis fit to each information input component is determined by the specification of the error covariance matrices in the data assimilation system (DAS). Weak-constraint 4D-Var (w4D-Var) provides a theoretical framework to account for modeling errors in the analysis scheme. In addition to the specification of the background error covariance matrix, the w4D-Var formulation requires information on the model error statistics and specification of the model error covariance. Up to now, the increased computational cost associated with w4D-Var has prevented its practical implementation. Various simplifications to reduce the computational burden have been considered, including writing the model error covariance as a scalar multiple of the background error covariance and modeling the model error. In this thesis, the main objective is the development of computationally feasible techniques for the improved representation of the model error statistics in a data assimilation system. Three new approaches are considered. A Monte Carlo method that uses an ensemble of w4D-Var systems to obtain flow-dependent estimates to the model error statistics. The evaluation of statistical diagnostic equations involving observation residuals to estimate the model error covariance matrix. An adaptive tuning procedure based on the sensitivity of a short-range forecast error measure to the model error DAS parametrization. The validity and benefits of these approaches are shown in two stages of numerical experiments. A proof-of-concept is shown using the Lorenz multi-scale model and the shallow water equations for a one-dimensional domain. The results show the potential of these methodologies to produce improved state estimates, as compared to other approaches in data assimilation. It is expected that the techniques presented will find an extended range of applications to assess and improve the performance of a w4D-Var system.
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Wyant, Timothy Joseph. "Numerical study of error propagation in Monte Carlo depletion simulations." Thesis, Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44809.

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Improving computer technology and the desire to more accurately model the heterogeneity of the nuclear reactor environment have made the use of Monte Carlo depletion codes more attractive in recent years, and feasible (if not practical) even for 3-D depletion simulation. However, in this case statistical uncertainty is combined with error propagating through the calculation from previous steps. In an effort to understand this error propagation, four test problems were developed to test error propagation in the fuel assembly and core domains. Three test cases modeled and tracked individual fuel pins in four 17x17 PWR fuel assemblies. A fourth problem modeled a well-characterized 330MWe nuclear reactor core. By changing the code's initial random number seed, the data produced by a series of 19 replica runs of each test case was used to investigate the true and apparent variance in k-eff, pin powers, and number densities of several isotopes. While this study does not intend to develop a predictive model for error propagation, it is hoped that its results can help to identify some common regularities in the behavior of uncertainty in several key parameters.
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Camacho, Fernando F. "A Posteriori Error Estimates for Surface Finite Element Methods." UKnowledge, 2014. http://uknowledge.uky.edu/math_etds/21.

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Problems involving the solution of partial differential equations over surfaces appear in many engineering and scientific applications. Some of those applications include crystal growth, fluid mechanics and computer graphics. Many times analytic solutions to such problems are not available. Numerical algorithms, such as Finite Element Methods, are used in practice to find approximate solutions in those cases. In this work we present L2 and pointwise a posteriori error estimates for Adaptive Surface Finite Elements solving the Laplace-Beltrami equation −△Γ u = f . The two sources of errors for Surface Finite Elements are a Galerkin error, and a geometric error that comes from replacing the original surface by a computational mesh. A posteriori error estimates on flat domains only have a Galerkin component. We use residual type error estimators to measure the Galerkin error. The geometric component of our error estimate becomes zero if we consider flat domains, but otherwise has the same order as the residual one. This is different from the available energy norm based error estimates on surfaces, where the importance of the geometric components diminishes asymptotically as the mesh is refined. We use our results to implement an Adaptive Surface Finite Element Method. An important tool for proving a posteriori error bounds for non smooth functions is the Scott-Zhang interpolant. A refined version of a standard Scott-Zhang interpolation bound is also proved during our analysis. This local version only requires the interpolated function to be in a Sobolev space defined over an element T instead of an element patch containing T. In the last section we extend our elliptic results to get estimates for the surface heat equation ut − △Γ u = f using the elliptic reconstruction technique.
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Czuprynski, Kenneth Daniel. "Numerical analysis in energy dependent radiative transfer." Diss., University of Iowa, 2017. https://ir.uiowa.edu/etd/5925.

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The radiative transfer equation (RTE) models the transport of radiation through a participating medium. In particular, it captures how radiation is scattered, emitted, and absorbed as it interacts with the medium. This process arises in numerous application areas, including: neutron transport in nuclear reactors, radiation therapy in cancer treatment planning, and the investigation of forming galaxies in astrophysics. As a result, there is great interest in the solution of the RTE in many different fields. We consider the energy dependent form of the RTE and allow media containing regions of negligible absorption. This particular case is not often considered due to the additional dimension and stability issues which arise by allowing vanishing absorption. In this thesis, we establish the existence and uniqueness of the underlying boundary value problem. We then proceed to develop a stable numerical algorithm for solving the RTE. Alongside the construction of the method, we derive corresponding error estimates. To show the validity of the algorithm in practice, we apply the algorithm to four different example problems. We also use these examples to validate our theoretical results.
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Books on the topic "Numerical error analysis"

1

Error analysis in numerical processes. Wiley, 1991.

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Shu, Lin. On codes with multi-level error-correction capabilities. National Aeronautics and Space Administration, 1987.

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Lin, Shu. On codes with multi-level error-correction capabilities. National Aeronautics and Space Administration, 1987.

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Numerical analysis for electromagnetic integral equations. Artech House, 2008.

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Baram, Yoram. Mean-square error bounds for reduced-order linear state estimators. National Aeronautics and Space Administration, Ames Research Center, 1987.

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Novak, Erich. Deterministic and stochastic error bounds in numerical analysis. Springer-Verlag, 1988.

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Novak, Erich. Deterministic and Stochastic Error Bounds in Numerical Analysis. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0079792.

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Shu, Lin. Cyclic unequal error protection codes constructed from cyclic codes of composite length. National Aeronautics and Space Administration, 1987.

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Kulisch, Ulrich. Numerical Toolbox for Verified Computing I: Basic Numerical Problems Theory, Algorithms, and Pascal-XSC Programs. Springer Berlin Heidelberg, 1993.

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1941-, Alefeld G., and Herzberger Jürgen, eds. Numerical methods and error bounds: Proceedings of the IMACS GAMM International Symposium on Numerical Methods and Error Bounds held in Oldenburg, Germany, July 9-12, 1995. Akademie Verlag, 1996.

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Book chapters on the topic "Numerical error analysis"

1

Stoer, J., and R. Bulirsch. "Error Analysis." In Introduction to Numerical Analysis. Springer New York, 2002. http://dx.doi.org/10.1007/978-0-387-21738-3_1.

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Stoer, J., and R. Bulirsch. "Error Analysis." In Introduction to Numerical Analysis. Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4757-2272-7_1.

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Hromadka, Theodore V., and Robert J. Whitley. "Numerical Error Analysis." In Advances in the Complex Variable Boundary Element Method. Springer London, 1998. http://dx.doi.org/10.1007/978-1-4471-3611-8_5.

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Lohar, Debasmita, Milos Prokop, and Eva Darulova. "Sound Probabilistic Numerical Error Analysis." In Lecture Notes in Computer Science. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-34968-4_18.

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Leffelaar, P. A. "Numerical integration and error analysis." In On Systems Analysis and Simulation of Ecological Processes. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2086-9_6.

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Leffelaar, P. A. "Numerical integration and error analysis." In On Systems Analysis and Simulation of Ecological Processes. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4814-6_6.

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Jakubovitz, Daniel, Raja Giryes, and Miguel R. D. Rodrigues. "Generalization Error in Deep Learning." In Applied and Numerical Harmonic Analysis. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-319-73074-5_5.

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Novak, Erich. "Deterministic error bounds." In Deterministic and Stochastic Error Bounds in Numerical Analysis. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0079794.

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Novak, Erich. "Average error bounds." In Deterministic and Stochastic Error Bounds in Numerical Analysis. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0079796.

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Zhou, You-He. "Error Analysis and Boundary Extension." In Wavelet Numerical Method and Its Applications in Nonlinear Problems. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-33-6643-5_4.

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Conference papers on the topic "Numerical error analysis"

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Alefeld, G. "Complementarity Problems: Error Bounds for Approximate Solutions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990973.

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Pötzelberger, Klaus. "Consistency of the empirical quantization error." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756158.

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Hollevoet, D., M. Van Daele, and G. Vanden Berghe. "On the Leading Error Term of Exponentially Fitted Numerov Methods." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991074.

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Hladík, Milan, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Error Bounds on the Spectral Radius of Uncertain Matrices." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636875.

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MURAI, Daisuke, Hideyuki AZEGAMI, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Error Analysis for a Regular Solution of Topology Optimization Problem." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637865.

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Calvo, M., P. Laburta, J. I. Montijano, and L. Rández. "On the Long Time Error of First Integrals of Some Numerical Integrators." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2991071.

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Selmi, Hassib, Hatem Hamda, Lassaad El Asmi, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Fast Multipole Method for the 3D Stokes Flow: Truncation Error Analysis and Asymptotic Complexity." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790189.

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Sebastianelli, S., F. Russo, F. Napolitano, and L. Baldini. "Assessment of an adjustment factor to model radar range dependent error." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756523.

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Stanić, Marija P., Aleksandar S. Cvetković, and Tatjana V. Tomović. "Error bounds for some quadrature rules with maximal trigonometric degree of exactness." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756324.

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Vlasák, Miloslav, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Optimal Error Estimates for Semi–implicit DG Time Discretization of Convection–Diffusion Problems." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636886.

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Reports on the topic "Numerical error analysis"

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Zoller, Miklos. Error Analysis on Numerical Integration Algorithms in a Hypoelasticity Framework. Office of Scientific and Technical Information (OSTI), 2021. http://dx.doi.org/10.2172/1806423.

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Ihlenburg, Frank, and Ivo Babuska. Dispersion Analysis and Error Estimation of Galerkin Finite Element Methods for the Numerical Computation of Waves. Defense Technical Information Center, 1994. http://dx.doi.org/10.21236/ada290296.

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Peralta-Alva, Adrian, and Manuel S. Santos. Analysis of Numerical Errors. Federal Reserve Bank of St. Louis, 2012. http://dx.doi.org/10.20955/wp.2012.062.

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Patel, Reena, David Thompson, Guillermo Riveros, Wayne Hodo, John Peters, and Felipe Acosta. Dimensional analysis of structural response in complex biological structures. Engineer Research and Development Center (U.S.), 2021. http://dx.doi.org/10.21079/11681/41082.

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The solution to many engineering problems is obtained through the combination of analytical, computational and experimental methods. In many cases, cost or size constraints limit testing of full-scale articles. Similitude allows observations made in the laboratory to be used to extrapolate the behavior to full-scale system by establishing relationships between the results obtained in a scaled experiment and those anticipated for the full-scale prototype. This paper describes the application of the Buckingham Pi theorem to develop a set of non-dimensional parameters that are appropriate for describing the problem of a distributed load applied to the rostrum of the paddlefish. This problem is of interest because previous research has demonstrated that the rostrum is a very efficient structural system. The ultimate goal is to estimate the response of a complex, bio-inspired structure based on the rostrum to blast load. The derived similitude laws are verified through a series of numerical experiments having a maximum error of 3.39%.
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