Relevant bibliographies by topics / Numerical differentiation

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

Academic literature on the topic 'Numerical differentiation'

Author: Grafiati
Published: 4 June 2021
Last updated: 30 July 2024

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Journal articles on the topic "Numerical differentiation"

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Riachy, Samer, Mamadou Mboup, and Jean-Pierre Richard. "Multivariate numerical differentiation." Journal of Computational and Applied Mathematics 236, no. 6 (October 2011): 1069–89. http://dx.doi.org/10.1016/j.cam.2011.07.031.

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Chartrand, Rick. "Numerical Differentiation of Noisy, Nonsmooth Data." ISRN Applied Mathematics 2011 (May 11, 2011): 1–11. http://dx.doi.org/10.5402/2011/164564.

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We consider the problem of differentiating a function specified by noisy data. Regularizing the differentiation process avoids the noise amplification of finite-difference methods. We use total-variation regularization, which allows for discontinuous solutions. The resulting simple algorithm accurately differentiates noisy functions, including those which have a discontinuous derivative.
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Obradovic, Dragan, Lakshmi Narayan Mishra, and Vishnu Narayan Mishra. "Numerical Differentiation and Integration." JOURNAL OF ADVANCES IN PHYSICS 19 (January 25, 2021): 1–5. http://dx.doi.org/10.24297/jap.v19i.8938.

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There are several reasons why numerical differentiation and integration are used. The function that integrates f (x) can be known only in certain places, which is done by taking a sample. Some supercomputers and other computer applications sometimes need numerical integration for this very reason. The formula for the function to be integrated may be known, but it may be difficult or impossible to find the antiderivation that is an elementary function. One example is the function f (x) = exp (−x2), an antiderivation that cannot be written in elementary form. It is possible to find antiderivation symbolically, but it is much easier to find a numerical approximation than to calculate antiderivation (anti-derivative). This can be used if antiderivation is given as an unlimited array of products, or if the budget would require special features that are not available to computers.
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Ramm, Alexander G., and Alexandra B. Smirnova. "On stable numerical differentiation." Mathematics of Computation 70, no. 235 (March 9, 2001): 1131–54. http://dx.doi.org/10.1090/s0025-5718-01-01307-2.

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Huang, Xiaowei, Chuansheng Wu, and Jun Zhou. "Numerical differentiation by integration." Mathematics of Computation 83, no. 286 (June 4, 2013): 789–807. http://dx.doi.org/10.1090/s0025-5718-2013-02722-6.

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Herceg, Dragoslav, and Ljiljana Cvetković. "On a Numerical Differentiation." SIAM Journal on Numerical Analysis 23, no. 3 (June 1986): 686–91. http://dx.doi.org/10.1137/0723044.

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Ling, Leevan, and Qi Ye. "On meshfree numerical differentiation." Analysis and Applications 16, no. 05 (August 30, 2018): 717–39. http://dx.doi.org/10.1142/s021953051850001x.

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We combine techniques in meshfree methods and Gaussian process regressions to construct kernel-based estimators for numerical derivatives from noisy data. Specially, we construct meshfree estimators from normal random variables, which are defined by kernel-based probability measures induced from symmetric positive definite kernels, to reconstruct the unknown partial derivatives from scattered noisy data. Our developed theories give rise to Tikhonov regularization methods with a priori parameter, but the shape parameters of the kernels remain tunable. For that, we propose an error measure that is computable without the exact values of the derivative. This allows users to obtain a quasi-optimal kernel-based estimator by comparing the approximation quality of kernel-based estimators. Numerical examples in two dimensions and three dimensions are included to demonstrate the convergence behavior and effectiveness of the proposed numerical differentiation scheme.
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Davydov, Oleg, and Robert Schaback. "Minimal numerical differentiation formulas." Numerische Mathematik 140, no. 3 (May 31, 2018): 555–92. http://dx.doi.org/10.1007/s00211-018-0973-3.

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Murphy, Robin. "103.45 Improving elementary numerical integration using numerical differentiation." Mathematical Gazette 103, no. 558 (October 21, 2019): 548–56. http://dx.doi.org/10.1017/mag.2019.127.

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Hanke, Martin, and Otmar Scherzer. "Inverse Problems Light: Numerical Differentiation." American Mathematical Monthly 108, no. 6 (June 2001): 512. http://dx.doi.org/10.2307/2695705.

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Dissertations / Theses on the topic "Numerical differentiation"

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Bodily, Chris H. "Numerical Differentiation Using Statistical Design." NCSU, 2002. http://www.lib.ncsu.edu/theses/available/etd-07082002-235127/.

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Derivatives are frequently required by numerical procedures across many disciplines. Numerical differentiation can be useful for approximating derivatives. This dissertation will introduce computational differentiation (the process by which derivatives are obtained with a computer), focusing on statistical response surface (RSM) designs for approximating derivatives. The RSM designs are compared with two competing numerical methods: namely a rival saturated statistical design approach, and a method employing finite differencing. A covariance model incorporating function curvature and computer round-off error is proposed for estimating the derivative approximation variances. These variances and the computational workload each method requires become the basis for comparing the derivative approximations. A diagnostic test for variable scaling errors is also described.
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Hu, Luoan 1954. "DBDF: An implicit numerical differentiation algorithm for integrated circuit simulation." Thesis, The University of Arizona, 1991. http://hdl.handle.net/10150/277918.

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Frequently, the design of integrated circuits cannot be accomplished by purely analytical techniques. Accurate and efficient algorithms for numerical circuit simulation are important tools. Several circuit simulators, such as SPICE, have been made available for this task. Contrary to many other applications of numerical system simulation, integrated circuit problems don't lend themselves to a formulation of state-space models, since the space charge in a p-n junction is a nonlinear and noninvertible function of the voltage across the junction. Therefore, it is necessary to employ numerical differentiation instead of numerical integration in this type of simulation study. The numerical algorithms employed in today's circuit simulators are fairly primitive. SPICE, for example, offers only two very simple implementations of the trapezoidal rule and of the backwards differentiation formula. This thesis describes the design and implementation of DBDF, a specification of a numerical method in Nordsieck format for solving circuit simulation problems. A formal stability and truncation error analysis are included.
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Hodson, Joshua D. "Numerical Analysis and Spanwise Shape Optimization for Finite Wings of Arbitrary Aspect Ratio." DigitalCommons@USU, 2019. https://digitalcommons.usu.edu/etd/7574.

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This work focuses on the development of efficient methods for wing shape optimization for morphing wing technologies. Existing wing shape optimization processes typically rely on computational fluid dynamics tools for aerodynamic analysis, but the computational cost of these tools makes optimization of all but the most basic problems intractable. In this work, we present a set of tools that can be used to efficiently explore the design spaces of morphing wings without reducing the fidelity of the results significantly. Specifically, this work discusses automatic differentiation of an aerodynamic analysis tool based on lifting line theory, a light-weight gradient-based optimization framework that provides a parallel function evaluation capability not found in similar frameworks, and a modification to the lifting line equations that makes the analysis method and optimization process suitable to wings of arbitrary aspect ratio. The toolset discussed is applied to several wing shape optimization problems. Additionally, a method for visualizing the design space of a morphing wing using this toolset is presented. As a result of this work, a light-weight wing shape optimization method is available for analysis of morphing wing designs that reduces the computational cost by several orders of magnitude over traditional methods without significantly reducing the accuracy of the results.
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Safiran, Niloofar Verfasser], Uwe [Akademischer Betreuer] Naumann, and Erika [Akademischer Betreuer] [Ábrahám. "Differentiation of numerical simulations with embedded nonlinear systems and integrals / Niloofar Safiran ; Uwe Naumann, Erika Ábrahám." Aachen : Universitätsbibliothek der RWTH Aachen, 2018. http://d-nb.info/1196018057/34.

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Othmane, Amine. "Contributions to numerical differentiation using orthogonal polynomials and its application to fault detection and parameter identification." Electronic Thesis or Diss., université Paris-Saclay, 2022. http://www.theses.fr/2022UPAST144.

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La reconstruction de grandeurs non mesurées de systèmes dynamiques se résume souvent à la connaissance de dérivées d'ordres arbitraires mais fini des variables connues du système. L'approximation de ces dérivées à partir de mesures perturbées est néanmoins connu pour être un problème complexe. Toutefois, des algorithmes de différentiation numérique basés sur des polynômes orthogonaux et des séries de Fourier généralisées tronquées peuvent le simplifier considérablement. Ces dérivateurs sont en effet robustes aux bruits de mesure et peuvent contribuer à la résolution de problèmes complexes dans le domaine de l'automatique. Néanmoins, la sélection des paramètres des dérivateurs ainsi que leurs implémentations en temps réel constituent des défis critiques lors de l'application de ces méthodes. Ce travail présente un cadre unifié pour la synthèse et l'analyse de dérivateurs basés sur des polynômes orthogonaux classiques. Des approches existantes sont davantage développées et leurs relations avec les méthodes établies sont analysées. Les dérivateurs basés sur les polynômes de Jacobi, également appelés dérivateurs algébriques, constituent une classe particulière des algorithmes étudiés dans ce travail. Des directives pour la sélection des paramètres sont déduites à partir des interprétations des filtres des dérivateurs afin d'obtenir les propriétés souhaitées dans le domaine fréquentiel. Une nouvelle approche de paramétrage basée sur un problème d'optimisation et nécessitant uniquement le signal mesuré est proposée. Lors de la discussion de l'implémentation en temps discret, la préservation des propriétés dans le domaine fréquentiel est abordée en détail. Une étude expérimentale compare les résultats issus des différents dérivateurs. Les approximations obtenues, la charge de calcul et les besoins de mémoire sont analysés et interprétés. Les deux dernières caractéristiques sont essentielles pour les applications en temps réel. L'application des dérivateurs dans le domaine de l'automatique est démontrée à l'aide de deux études expérimentales pour la détection de défauts avec des algorithmes basés sur des modèles physiques. Tout d'abord, la collision d'une balle de ping-pong avec une plaque à lévitation magnétique est discutée. Seules la mesure de la position de la plaque et les forces appliquées sont disponibles. L'approche proposée réduit considérablement le temps de calcul et les besoins en mémoire comparée aux méthodes considérées jusqu'à présent. En outre, la nouvelle approche réduit la hauteur de chute minimale détectable de la balle. Ensuite, une approche est proposée pour une détection efficace et en temps réel des défauts dans des roulements. Cette méthode est validée à l'aide de données expérimentales provenant de différents bancs d'essai. Des approches d'estimation de paramètres sont ensuite discutées. Ce travail généralise des algorithmes récemment proposés. Les conditions de convergence dérivées sont moins restrictives que celles publiées précédemment. De plus, cette approche permet d'identifier un sous-ensemble de paramètres, même si certains ne sont pas excités. Deux études expérimentales valident l'analyse théorique. Les résultats sont comparés à ceux obtenus avec des estimateurs établis et des méthodes algébriques d'estimation des paramètres. Ces exemples confirment les potentiels de ces méthodes développées dans ce travail
The reconstruction of unmeasured quantities in dynamical systems often boils down to the knowledge of derivatives of the measured system variables. The approximation of these derivatives in the presence of measurement disturbances is known to be challenging. However, numerical differentiation algorithms based on orthogonal polynomials and truncated generalised Fourier series may considerably simplify the problem. These differentiators are robust to measurement disturbances and may contribute to solving complex control engineering tasks. Critical challenges for the application of the methods are the selection of favourable parameters and their real-time implementation. This work presents a unified framework for synthesizing and analysing differentiators based on classical orthogonal polynomials. Existing approaches are extended, and their relations to established methods are investigated. Differentiators based on Jacobi polynomials, also known as algebraic differentiators, form a particular class of the considered algorithms. Parameter selection guidelines are derived based on filter interpretations of the differentiators to achieve desired frequency-domain properties. The discussion of the discrete-time implementation emphasizes the preservation of the latter properties. A new tuning approach based on an optimization problem which requires only the measured signal is proposed. An experimental case study compares the performance of the differentiators in the presence of measurement disturbances. The approximation results, the computational burden, and the storage requirements are discussed in detail. Especially the latter two properties are crucial for real-time applications. The differentiators are used for model-based fault detection problems in two experimental case studies. First, the collision of a table tennis ball with a magnetically supported plate is discussed. Only the measurement of the plate position and the applied forces are known. The proposed approach significantly reduces the computational burden and memory requirements when compared to previously considered methods. Besides, the new approach decreases theminimum detectable falling height of the ball. Then, a model-based approach for the efficient real-time detection of faults in rolling element bearings is proposed. The approach is validated using experimental data from different test benches. Finally, a parameter estimation problem is discussed. This work generalises recently proposed algorithms. The derived convergence conditions are less restrictive than the previously published ones. Besides, this approach allows identifying a subset of parameters even if some are not excited. Two experimental case studies validate the theoretical analysis. The results are compared to those achieved using standard gradient estimators and algebraic parameter estimation methods. These examples underline the great potential of these methods
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Tateneni, Krishna. "Use of automatic and numerical differentiation in the estimation of asymptotic standard errors in exploratory factor analysis /." The Ohio State University, 1998. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487950658548932.

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Heller, Richard. "Checkpointing without operating system intervention implementing Griewank's algorithm." Ohio : Ohio University, 1998. http://www.ohiolink.edu/etd/view.cgi?ohiou1176494831.

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Birkisson, Asgeir. "Numerical solution of nonlinear boundary value problems for ordinary differential equations in the continuous framework." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:1df19052-5eb3-4398-a7b2-b103e380ec2c.

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Ordinary differential equations (ODEs) play an important role in mathematics. Although intrinsically, the setting for describing ODEs is the continuous framework, where differential operators are considered as maps from one function space to another, common numerical algorithms for ODEs discretise problems early on in the solution process. This thesis is about continuous analogues of such discrete algorithms for the numerical solution of ODEs. This thesis shows how Newton's method for finite dimensional system can be generalised to function spaces, where it is known as Newton-Kantorovich iteration. It presents affine invariant damping strategies for increasing the chance of convergence for the Newton-Kantorovich iteration. The derivatives required in this continuous setting are Fréchet derivatives, the continuous analogue of Jacobian matrices. In this work, we present how automatic differentiation techniques can be applied to compute Fréchet derivatives. We introduce chebop, a Matlab solver for nonlinear boundary-value problems, which combines damped Newton iteration in function space and automatic Fréchet differentiation. By proving that affine operators have constant Fréchet derivatives, it is demonstrated how automatic linearity detection of computed quantities can be implemented. This is valuable for black-box solvers, which can use the information to determine whether an iteration scheme has to be employed for solving a problem. Like nonlinear systems of equations, nonlinear boundary-value problems can have multiple solutions. This thesis present two techniques for obtaining multiple solutions of operator equations: deflation and path-following. An algorithm combining the two techniques is proposed.
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Pantland, Nicolette Ariana. "3D numerical techniques for determining the foot of a continental slope." Thesis, Stellenbosch : Stellenbosch University, 2004. http://hdl.handle.net/10019.1/49807.

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Thesis (MSc)--University of Stellenbosch, 2004.
ENGLISH ABSTRACT: The United Nations Convention on the Law of the Sea (UNCLOS) provides an opportunity for qualifying coastal signatory states to claim extended maritime estate. The opportunity to claim rests on the precept that in certain cases a continental shelf extends beyond the traditionally demarcated two hundred nautical mile (200M) Exclusive Economic Zone (EEZ) mark. In these cases a successful claim results in states having sovereign rights to the living and non-living resources of the seabed and subsoil, as well as the sedentary species, of the area claimed. Where the continental shelf extends beyond the 200M mark, the Foot of the Continental Slope (FoS) has to be determined as one of the qualifying criteria. Article 76 of UNCLOS de nes the FoS as ". . . the point of maximum change in the gradient at its base." Currently Caris Lots is the most widely used software which incorporates public domain data to determine the FoS as a step towards defining the offshore extent of an extended continental shelf. In this software, existing methods to compute the FoS are often subjective, typically involving an operator choosing the best perceived foot point during consideration of a two dimensional profile of the continental slope. These foot points are then joined by straight lines to form the foot line to be used in the desk top study (feasibility study). The purpose of this thesis is to establish a semi-automated and mathematically based three dimensional method for determination of the FoS using South African data as a case study. Firstly, a general background of UNCLOS is given (with emphasis on Article 76), including a brief discussion of the geological factors that influence the characteristics of a continental shelf and thus factors that could influence the determination of the FoS. Secondly, a mathematical method for determination of the surfaces of extremal curvature (on three dimensional data), originally proposed by Vanicek and Ou in 1994, is detailed and applied to two smooth, hypothetical sample surfaces. A discussion of the bathymetric data to be used for application introduces the factors to be taken into account when using extensive survey data as well as methods to process the raw data for use. The method is then applied to two sets of gridded bathymetric data of differing resolution for four separate regions around the South African coast. The ridges formed on the resulting surfaces of maximum curvature are then traced in order to obtain a foot line definition for each region and each resolution. The results obtained from application of the method are compared with example foot points provided by the subjective two dimensional method of computation within the Caris Lots software suite. A comparison of the results for the different resolutions of data is included to provide insight as to the effectiveness of the method with differing spatial coarseness of data. Finally, an indication of further work is provided in the conclusion to this thesis, in the form of a number of recommendations for possible adaptations of the mathematical and tracing methods, and improvements thereof.
AFRIKAANSE OPSOMMING: Die Verenigde Nasies se Konvensie oor die Wet van die See (UNCLOS) bied 'n geleentheid aan kwalifiserende state wat ondertekenaars van die Konvensie is om aanspraak te maak op uitgebreide maritieme gebied. Die geleentheid om op uitgebreide gebied aanspraak te maak berus op die veronderstelling dat 'n kontinentale tafel in sekere gevalle tot buite die tradisioneel afgebakende 200 seemyl eksklusiewe ekonomiese zone (EEZ) strek. In sulke gevalle het 'n suksesvolle aanspraak die gevolg dat die staat soewereine reg oor die lewende en nie-lewende bronne van die seevloer en ondergrond verkry, sowel as die inwonende spesies van die gebied buite die EEZ waarop aanspraak gemaak word. Die voet van die kontinentale tafel (FoS) moet vasgestel word as een van die bepalende kriteria vir afbakening van die aanspraak waar die kontinentale tafel tot buite die EEZ strek. Artikel 76 van UNCLOS defineer die FoS as ". . . die punt van maksimale verandering in die helling by sy basis." Die mees algemeen gebruikte rekenaar sagteware wat openbare domein data aanwend om die voet van die helling te bepaal, is tans "Caris Lots." Die metodes wat in die program gebruik word om die voet van die helling te bepaal, is dikwels subjektief en berus tipies op 'n operateur se keuse van die beste afgeskatte punt van die voet van die helling uit 'n oorweging van 'n twee dimensionele profiel van die kontinentale tafel. Die berekende voet-punte word dan deur middel van reguit lyne verbind om 'n hellingsvoetlyn te vorm. Hierdie voetlyn kan dan in die Suid-Afrikaanse lessenaarstudie (doenlikheidstudie) oor die bepaling van die voet van die kontinentale tafel gebruik word. Die doel van hierdie verhandeling is om 'n semi-outomatiese en wiskundig gebaseerde drie-dimensionele metode te beskryf vir die vasstelling van die FoS, deur as 'n gevallestudie van Suid-Afrikaanse data gebruik te maak. 'n Algemene agtergrond van UNCLOS, met beklemtoning van Artikel 76, word eerstens gegee. 'n Kort bespreking van die geologiese faktore wat die kontinentale tafel beïnvloed en wat gevolglik 'n invloed kan hê op die vasstelling van die voet van die helling, is ingesluit. Tweedens word 'n wiskundige metode, wat oorspronklik in 1994 deur Vanicek en Ou voorgestel is, vir bepaling van die oppervlaktes van maksimale kromming (gebaseer op drie-dimensionele data) in detail bespreek en 'n voorbeeld van 'n toepassing op twee gladde, denkbeeldige oppervaktes word beskryf. Die faktore wat in ag geneem moet word wanneer omvattende dieptemeting data gebruik word, en die metodes wat gebruik word om die rou data te verwerk, word ingelei deur 'n bespreking van die aard van die dieptemeting data wat gebruik is. Die metode word dan toegepas op twee stelle geruite dieptemeting data van verskillende resolusies vir vier afsonderlike streke om die Suid-Afrikaanse kus. Die riwwe wat op die resulterende oppervlaktes van maksimale kromming gevorm word, word dan nagetrek ten einde 'n lyndefinisie van die voet van die kontinentale tafel vir elke streek teen elke resolusie te bepaal. Die resultate verkry uit toepassings van die metode word vergelyk met hellingsvoetpunte soos bepaal deur die subjektiewe twee dimensionele berekeningsmetode in die "Caris Lots" rekenaar-program. 'n Vergelyking van die resultate vir die verskillende data resolusies word ingesluit om die doeltreffendheid van die metode met betrekking tot die hantering van verskillende ruimtelike data resolusies te ondersoek. 'n Aanduiding van verdere werk, bestaande uit 'n aantal aanbevelings vir moontlike aanpassings en verbeterings van die wiskundige en natrek metodes, word ten slotte in die gevolgtrekking van die verhandeling verskaf.
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Stary, Tomas. "Mathematical and computational study of Markovian models of ion channels in cardiac excitation." Thesis, University of Exeter, 2016. http://hdl.handle.net/10871/24166.

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This thesis studies numerical methods for integrating the master equations describing Markov chain models of cardiac ion channels. Such models describe the time evolution of the probability that ion channels are in a particular state. Numerical simulations of such models are often computationally demanding because many solvers require relatively small time steps to ensure numerical stability. The aim of this project is to analyse selected Markov chains and develop more efficient and accurate solvers. We separate a Markov chain model into fast and slow time-scales based on the speed of transitions between states. Eliminating the fast transitions, we find an asymptotic reduction of zeroth-order and first-order in a small parameter describing the time-scales separation. We apply the theory to a Markov chain model of the fast sodium channel INa. We consider several variants for classifying some transitions as fast in order to find reduced systems that yield a good accuracy. However, the time step size is still restricted by numerical instabilities. We adapt the Rush-Larsen technique originally developed for gate models. Assuming that a transition matrix can be considered constant during each time step, we solve the Markov chain model analytically. The solution provides a recipe for a stable exponential solver, which we call "Matrix Rush-Larsen" (MRL). Using operator splitting we design an even more flexible "hybrid" method that combines the MRL with other solvers. The resulting improvement in stability allows a large increase in the time step size. In some models, we obtain reasonably accurate results 27 times faster using a hybrid method than with the forward Euler method, even with the maximal time step allowed by the stability constraint. Finally, we extend the cardiac simulation package BeatBox by the developed exponential solvers. We upgrade a format of "ionic" modules which describe a cardiac cell, in order to allow for a specific definition of Markov chain models. We also modify a particular integrator for ionic modules to include the MRL and the hybrid method. To test the functionality of the code, we have converted a number of cellular models into the ionic format. The documented code is available in the official BeatBox package distribution.
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Books on the topic "Numerical differentiation"

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Owolabi, Kolade M., and Abdon Atangana. Numerical Methods for Fractional Differentiation. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-15-0098-5.

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Bitterlich, Walter. Numerische Methoden für technische Berechnungen. Aachen: Shaker Verlag, 2004.

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Kai, Diethelm, Luchko Yury, and NASA Glenn Research Center, eds. Fractional-order viscoelasticity (FOV): Constitutive development using the fractional calculus : first annual report. [Cleveland, Ohio]: National Aeronautics and Space Administration, Glenn Research Center, 2002.

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Kai, Diethelm, Luchko Yury, and NASA Glenn Research Center, eds. Fractional-order viscoelasticity (FOV): Constitutive development using the fractional calculus : first annual report. [Cleveland, Ohio]: National Aeronautics and Space Administration, Glenn Research Center, 2002.

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Freed, Alan. Fractional-order viscoelasticity (FOV): Constitutive development using the fractional calculus : first annual report. [Cleveland, Ohio]: National Aeronautics and Space Administration, Glenn Research Center, 2002.

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Skeel, Robert D. Global error estimation and the backward differentiation formulas. Urbana, IL (1304 W. Springfield Ave., Urbana 61801): Dept. of Computer Science, University of Illinois at Urbana-Champaign, 1986.

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Treanţă, Savin. Variational analysis with applications in optimisation and control. Newcastle upon Tyne, UK: Cambridge Scholars Publishing, 2019.

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Verma, Arun. On the efficient methods to solve ODEs and BVPs using automatic differentiation. Ithaca, N.Y: Cornell Theory Center, Cornell University, 1996.

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Glovackaya, Alevtina. Computational model. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1013723.

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The textbook covers the basics of classical numerical methods of computational mathematics used for solving linear and nonlinear equations and systems; interpolation and approximation of functions; numerical integration and differentiation; solutions of ordinary differential equations by methods of one-dimensional and multidimensional optimization. Meets the requirements of the Federal state educational standards of higher education of the latest generation. It is intended for students of higher educational institutions studying in the discipline "Numerical methods".
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Dolgov, I., Mihail Volovik, and Andrey Mahnovskiy. Thermographic signs of certain diseases of the respiratory system (acute sinusitis, pneumonia) Thermography Atlas. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/textbook_61b1ab7de6b1f9.69203696.

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The present issue focuses on the practice of medical thermal imaging in patients with paranasal sinusitis and pneumonia. The description of thermograms is based on a quantitative analysis of temperature gradients and trends in temperature of different body regions (Projection «head front» for paranasal sinusitis, «breast front» and «back», in a defined layout formed in «cloud» thermograms analysis program "Tvision" of «Dignosis», Russia) with values of thermographic markers that demonstrated their differentiating capabilities when compared with reference methods. Thus, the thermographic conclusion is formed not simply by thermal phenomenon «hot-cold», but on the basis of numerical values of markers, which indicate hypothetical nosological diagnosis and significantly simplifies the algorithm for those physicians who use this method as an additional. The publication is intended for doctors of any speciality who, in their daily clinical practice, treat the patients with suspicions disease of respiratory system
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Book chapters on the topic "Numerical differentiation"

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Scherer, Philipp O. J. "Numerical Differentiation." In Graduate Texts in Physics, 39–46. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-61088-7_3.

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Woodford, C., and C. Phillips. "Numerical Differentiation." In Numerical Methods with Worked Examples: Matlab Edition, 119–33. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-1366-6_6.

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Anastassiou, George A., and Razvan A. Mezei. "Numerical Differentiation." In Springer Undergraduate Texts in Mathematics and Technology, 161–73. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16739-8_4.

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Scherer, Philipp O. J. "Numerical Differentiation." In Computational Physics, 29–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-13990-1_3.

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Engeln-Müllges, Gisela, and Frank Uhlig. "Numerical Differentiation." In Numerical Algorithms with C, 353–60. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-61074-5_14.

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Engeln-Müllges, Gisela, and Frank Uhlig. "Numerical Differentiation." In Numerical Algorithms with Fortran, 353–60. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-80043-6_14.

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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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Saha Ray, Santanu. "Numerical Differentiation." In Numerical Analysis with Algorithms and Programming, 159–83. Boca Raton : Taylor & Francis, 2016. | “A CRC title.”: Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9781315369174-4.

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Faul, A. C. "Numerical Differentiation." In A Concise Introduction to Numerical Analysis, 205–9. Boca Raton : Taylor & Francis, 2016. | “A CRC title.”: Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9781315370217-7.

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Scherer, Philipp O. J. "Numerical Differentiation." In Graduate Texts in Physics, 37–43. Heidelberg: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00401-3_3.

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Conference papers on the topic "Numerical differentiation"

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Giménez Palomares, Fernando, Juan Antonio Monsoriu Serrá, and Jose Fernando Giménez Luján. "NUMERICAL DIFFERENTIATION: A VIRTUAL LABORATORY." In International Technology, Education and Development Conference. IATED, 2017. http://dx.doi.org/10.21125/inted.2017.2212.

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Harker, Matthew, and Paul O'Leary. "Polynomial accurate numerical fractional order integration and differentiation." In 2014 International Conference on Fractional Differentiation and its Applications (ICFDA). IEEE, 2014. http://dx.doi.org/10.1109/icfda.2014.6967402.

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Qian, Ailin, and Yan Li. "A modified method for fractional numerical differentiation." In 2011 International Conference on Information Science and Technology (ICIST). IEEE, 2011. http://dx.doi.org/10.1109/icist.2011.5765197.

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Zhao, Zhenyu, and Lei You. "Numerical Differentiation by Legendre-Gauss-Lobatto Interpolation." In 2010 International Conference on Computational and Information Sciences (ICCIS). IEEE, 2010. http://dx.doi.org/10.1109/iccis.2010.196.

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Chartrand, Rick. "Numerical differentiation of noisy, nonsmooth, multidimensional data." In 2017 IEEE Global Conference on Signal and Information Processing (GlobalSIP). IEEE, 2017. http://dx.doi.org/10.1109/globalsip.2017.8308641.

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Zhou, Wen, Yiwen Liang, Hongbin Dong, Chengyu Tan, Zhenhua Xiao, and Weiwei Liu. "A Numerical Differentiation Based Dendritic Cell Model." In 2017 IEEE 29th International Conference on Tools with Artificial Intelligence (ICTAI). IEEE, 2017. http://dx.doi.org/10.1109/ictai.2017.00167.

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Chen, Ming-Da, Tung-Ju Hsieh, and Yang-Lang Chang. "Volume Data Numerical Integration and Differentiation Using CUDA." In 2011 IEEE 17th International Conference on Parallel and Distributed Systems (ICPADS). IEEE, 2011. http://dx.doi.org/10.1109/icpads.2011.148.

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Tay, Kim Gaik, Sie Long Kek, and Rosmila Abdul-Kahar. "Improved Richardson’s extrapolation spreadsheet calculator for numerical differentiation." In PROCEEDINGS OF THE 21ST NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM21): Germination of Mathematical Sciences Education and Research towards Global Sustainability. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4887682.

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"Two numerical differentiation techniques for nonlinear state estimation." In Proceedings of the 1999 American Control Conference. IEEE, 1999. http://dx.doi.org/10.1109/acc.1999.782871.

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Diop, S., V. Fromion, and J. W. Grizzle. "A resettable Kalman filter based on numerical differentiation." In 2001 European Control Conference (ECC). IEEE, 2001. http://dx.doi.org/10.23919/ecc.2001.7076086.

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Reports on the topic "Numerical differentiation"

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GOSSLER, ALBERT A. Moving Least-Squares: A Numerical Differentiation Method for Irregularly Spaced Calculation Points. Office of Scientific and Technical Information (OSTI), June 2001. http://dx.doi.org/10.2172/782717.

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GOSSLER, ALBERT A. Moving Least-Squares: A Numerical Differentiation Method for Irregularly Spaced Calculation Points. Office of Scientific and Technical Information (OSTI), June 2001. http://dx.doi.org/10.2172/782718.

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Judd, Kenneth L., and Ben Skrainka. High performance quadrature rules: how numerical integration affects a popular model of product differentiation. Institute for Fiscal Studies, February 2011. http://dx.doi.org/10.1920/wp.cem.2011.0311.

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