Filters








29,107 Hits in 5.1 sec

Linear Approximation of Continuous Systems with Trapezoid Step Functions [chapter]

Giulia Costantini, Pietro Ferrara, Agostino Cortesi
<span title="">2012</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We introduce a novel abstract domain for the safe approximation of continuous functions in the context of abstract interpretationbased static analysis.  ...  The key-idea is to represent C 2 + functions by a finite sequence of trapezoids.  ...  The two linear functions, together with the two vertical lines that delimit the time slot, form a trapezoid. We approximate the function with a finite number of trapezoids, one for each step.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-35182-2_8">doi:10.1007/978-3-642-35182-2_8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2npnwunzpnfppfm76xqler2xsm">fatcat:2npnwunzpnfppfm76xqler2xsm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706073301/http://www.dsi.unive.it/~cortesi/paperi/APLAS2012.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e4/aa/e4aa0f43b0f83209cde3a9f07c074308b1290294.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-35182-2_8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

A Numerical Method for Fuzzy Differential Equations and Hybrid Fuzzy Differential Equations

K. Ivaz, A. Khastan, Juan J. Nieto
<span title="">2013</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dgcr32e3abazpn7i4ocwedp3fa" style="color: black;">Abstract and Applied Analysis</a> </i> &nbsp;
Sufficient conditions for stability and convergence of the proposed algorithms are given, and their applicability is illustrated with some examples.  ...  This research was completed during the visit of the second author to the USC.  ...  Acknowledgments The first author would like to thank the financial support of the Islamic Azad University, Shabestar Branch.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2013/735128">doi:10.1155/2013/735128</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qtfghleymbbnviuzbyfvk77zsu">fatcat:qtfghleymbbnviuzbyfvk77zsu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170814124804/http://downloads.hindawi.com/journals/aaa/2013/735128.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d7/ea/d7ea5802ddec3f377926bce3268440cc1dd165a5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2013/735128"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> hindawi.com </button> </a>

On conjugate difference schemes: the midpoint scheme and the trapezoidal scheme

Yu Ying, Mikhail D. Malykh
<span title="2021-12-15">2021</span> <i title="Peoples&#39; Friendship University of Russia"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nfajb3h5yrhn5ljxxkek2vvuha" style="color: black;">Discrete and Continuous Models and Applied Computational Science</a> </i> &nbsp;
The preservation of quadratic integrals on approximate solutions of autonomous systems of ordinary differential equations x=f(x), found by the trapezoidal scheme, is investigated.  ...  The results are illustrated by examples of linear and elliptic oscillators. In both cases, expressions preserved by the trapezoidal scheme are presented explicitly.  ...  Relationship between trapezoidal and midpoint schemes The approximate solution of the system (1), found by the scheme (2) with constant step Δ , is a finite or infinite sequence of points 0 , 1 , 2 , …  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.22363/2658-4670-2021-29-1-63-72">doi:10.22363/2658-4670-2021-29-1-63-72</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mgv5gy52gba4lpxo3v7abep3t4">fatcat:mgv5gy52gba4lpxo3v7abep3t4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210715125635/http://journals.rudn.ru/miph/article/download/26141/19261" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/89/86/8986568cbbe7bef9a2d311659151a8e736994476.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.22363/2658-4670-2021-29-1-63-72"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Integrating Lipschitzian Dynamical Systems using Piecewise Algorithmic Differentiation [article]

Andreas Griewank and Richard Hasenfelder and Manuel Radons and Tom Streubel
<span title="2017-01-03">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Moreover, the method is energy preserving for piecewise linear Hamiltonian systems.  ...  The advantage of the proposed generalized trapezoidal rule is threefold: Firstly we can achieve a higher convergence order than with the classical method.  ...  Acknowledgements The work for the article has been partially conducted within the Research Campus MODAL funded by the German Federal Ministry of Education and Research (BMBF) (fund number 05M14ZAM).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1701.00745v1">arXiv:1701.00745v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/v7qzeahtb5bkna2w3jtnbpjvom">fatcat:v7qzeahtb5bkna2w3jtnbpjvom</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200905172330/https://arxiv.org/pdf/1701.00745v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7b/9a/7b9a5c5f5c607037867f6c4b4ae5f9673e8b3707.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1701.00745v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Linear System Of Equations With Trapezoidal Fuzzy Numbers

S.h. Nasseri, M. Gholami
<span title="2011-07-20">2011</span> <i title="International Scientific Research Publications MY SDN. BHD."> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bmhn5xzzqzfevooumwiffmuzfm" style="color: black;">Journal of Mathematics and Computer Science</a> </i> &nbsp;
In this paper, we introduce a linear system of equations with trapezoidal fuzzy numbers as an extension of the fuzzy linear systems which was first introduced by Friedman et al. [6] .  ...  Conditions for the existence of a trapezoidal fuzzy solution to n × n linear system are derived and a numerical procedure for calculating the solution is illustrated with some examples.  ...  In this paper, we introduce a linear system of equations with trapezoidal fuzzy numbers as an extension of the common fuzzy linear system of equations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.22436/jmcs.03.01.06">doi:10.22436/jmcs.03.01.06</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/axd4kfvpibbw7fhd2x3o6ggmbu">fatcat:axd4kfvpibbw7fhd2x3o6ggmbu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190501222158/https://www.isr-publications.com/jmcs/167/download-linear-system-of-equations-with-trapezoidal-fuzzy-numbers" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/89/df/89df9edd41c7242bcfa81cafe69a0d3cc9556775.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.22436/jmcs.03.01.06"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Trapezoidal methods of approximating solutions of differential equations

Preston C. Hammer, Jack W. Hollingsworth
<span title="1955-09-01">1955</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5bz4zmidbngqxk6yv4msbkm54u" style="color: black;">Mathematics of Computation</a> </i> &nbsp;
Milne [1] p. 24) as a parabolic or quadratic function method, not only does one obtain a satisfying geometrical picture of an approximation curve in the usual case, but that two new trapezoidal or parabolic  ...  The authors, collaborating as a professor and student team, have found that the straightforward selection of functions to approximate solution functions offers many advantages conceptually and makes it  ...  Continuation of the solution method through several steps gives this picture: the approximating curve consists of continuously and smoothly joined parabolic arcs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0025-5718-1955-0072547-2">doi:10.1090/s0025-5718-1955-0072547-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6k23pae72nfw7i6ycnk57mbkhi">fatcat:6k23pae72nfw7i6ycnk57mbkhi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170820074639/http://www.ams.org/journals/mcom/1955-09-051/S0025-5718-1955-0072547-2/S0025-5718-1955-0072547-2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ef/a0/efa02127370463c62ac3abaf17dd62d5a6264a6f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0025-5718-1955-0072547-2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Scale-selective Time Integration for Long-Wave Linear Acoustics [chapter]

Stefan Vater, Rupert Klein, Omar M. Knio
<span title="">2011</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/har7ss6cmjfsflxrcnqkhv5msm" style="color: black;">Springer Proceedings in Mathematics</a> </i> &nbsp;
In this note, we present a new method for the numerical integration of one dimensional linear acoustics with long time steps.  ...  It is based on a scale-wise decomposition of the data using standard multigrid ideas and a scale-dependent blending of basic time integrators with different principal features.  ...  Acknowledgements R.K. thanks Piotr Smolarkiewicz for stimulating and challenging discussions on the theme of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-20671-9_81">doi:10.1007/978-3-642-20671-9_81</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/i7g2ikhkmfdxbfxus6bpp36nou">fatcat:i7g2ikhkmfdxbfxus6bpp36nou</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200322113230/http://publications.imp.fu-berlin.de/1033/1/Vater2011ScaleSelectiveTimeIntegrationFVCA6.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f8/90/f890b2e200e402e4fcaa6a117d35991418797328.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-20671-9_81"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

DISCRETE-TIME MODEL FOR LINEAR CONTINUOUS-TIME REPETITIVE SYSTEM

J.E. Kurek
<span title="">2005</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p3wtlm3j2fedxitkuu4bs3scau" style="color: black;">IFAC Proceedings Volumes</a> </i> &nbsp;
Model is calculated based on the zero order hold on input approach and trapezoidal approximation of output signal on input to the state equation. Numerical examples are presented.  ...  A discrete-time model is proposed for continuous-time repetitive process.  ...  We will deal with the problem of calculation of discrete-time model for continuous-time linear repetitive system.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3182/20050703-6-cz-1902.00269">doi:10.3182/20050703-6-cz-1902.00269</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/inix43pqffdyvjm36qhdbnquve">fatcat:inix43pqffdyvjm36qhdbnquve</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706121547/http://folk.ntnu.no/skoge/prost/proceedings/ifac2005/Fullpapers/04141.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7a/ed/7aedc1b5c863321a18dcd66af7bd6943302ca5c1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3182/20050703-6-cz-1902.00269"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

DISCRETE APPROXIMATION OF CONTINUOUS OBJECTS WITH MATLAB

Olga Ivanivna Tolochko, Stefan Palis, Oleksii Olegovich Burmelov, Danylo Vladyslavovych Kaluhin
<span title="2021-06-30">2021</span> <i title="Odessa Polytechnic State University"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/sdmlhwanovdh5lik3d4iv2mtxe" style="color: black;">Applied Aspects of Information Technology</a> </i> &nbsp;
This work is dedicated to the study of various discrete approximation methods for continuous links, which is the obligatory step in the digital control systems synthesis for continuous dynamic objects  ...  The paper presents examples of using numerical and symbolic instruments of the MATLAB to perform these opera tions, offers an m-function improved version for continuous systems discretization by the zero-pole  ...  Impulse response () wt of the original continuous system with the transfer function ( 14 ) and discrete systems with the transfer functions ( 16 )- (18) are shown in Fig. 1 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.15276/aait.02.2021.5">doi:10.15276/aait.02.2021.5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jwhdlojmd5g7besrz23tszk2iy">fatcat:jwhdlojmd5g7besrz23tszk2iy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220209095019/http://aait.ccs.od.ua/index.php/journal/article/download/107/160/267" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e1/a1/e1a1a62dedf36b26ce7ac66d7affa5b2aac1f11d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.15276/aait.02.2021.5"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Asymptotic expansion for the trapezoidal Nyström method of linear Volterra—Fredholm equations

Han Guoqiang, Zhang Liqing
<span title="">1994</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/av75skmu6neednu63f27tpk7qu" style="color: black;">Journal of Computational and Applied Mathematics</a> </i> &nbsp;
In the present paper, we study the particular trapezoidal Nystrom method and we obtain the asymptotic error expansion for the trapezoidal Nystrom solution of the linear Volterra-Fredholm equation.  ...  Integral equations of mixed Volterra-Fredholm type arise in various physical and biological problems.  ...  Acknowledgements The authors are grateful to the two referees whose valuable suggestions led to a considerably improved version of the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0377-0427(92)00013-y">doi:10.1016/0377-0427(92)00013-y</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ljxtuswvbfapfnmhwzycpwrimy">fatcat:ljxtuswvbfapfnmhwzycpwrimy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190326155210/https://core.ac.uk/download/pdf/82759636.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/81/04/8104840403d6bdbcbe29f74ab7c56022f55fd944.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0377-0427(92)00013-y"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Adaptive integration of molecular dynamics

Illia Horenko, Martin Weiser
<span title="2003-09-23">2003</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/72zcmi3smndcrdvxgve7ny6ytq" style="color: black;">Journal of Computational Chemistry</a> </i> &nbsp;
For time integration, the implicit trapezoidal rule is employed, where an explicit predictor enables large time steps.  ...  The framework is developed and exemplified in the context of the classical Liouville equation, where Gaussian phase-space packets are used as particles. Simplified variants are discussed briefly.  ...  Schmidt for careful reading of the manuscript.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/jcc.10335">doi:10.1002/jcc.10335</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/14515374">pmid:14515374</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lvs42uw6mfh7dgmw7vg7gcng3e">fatcat:lvs42uw6mfh7dgmw7vg7gcng3e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20081031184427/http://biocomputing.mi.fu-berlin.de/publications/HoWe03.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a4/79/a479ac1f1078f2e241c848650b9616b447fd6bb1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/jcc.10335"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> wiley.com </button> </a>

Application of Splines of the Second Order Approximation to Volterra Integral Equations of the Second Kind. Applications in Systems Theory and Dynamical Systems

I. G. Burova, G. O. Alcybeev
<span title="2021-02-09">2021</span> <i title="North Atlantic University Union (NAUN)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pozhhqfrgbdn7cv2fsvqjd7gva" style="color: black;">North atlantic university union: International Journal of Circuits, Systems and Signal Processing</a> </i> &nbsp;
This paper discusses the application of local interpolation splines of the second order of approximation for the numerical solution of Volterra integral equations of the second kind.  ...  The application of splines to the solution of nonlinear Volterra integral equations is also discussed. The results of numerical experiments are presented  ...  The linear Volterra equation of the second kind has the form: ( ) + ∫ ( , ) ( ) = ( ), ∈ [ , ], (1) where ƒ is a given function, , are continuous functions and ( ) is an unknown function.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.46300/9106.2021.15.8">doi:10.46300/9106.2021.15.8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wj5zgl62lrbvrov456iftwgsaa">fatcat:wj5zgl62lrbvrov456iftwgsaa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210212085259/https://www.naun.org/main/NAUN/circuitssystemssignal/2021/a162005-008(2021).pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ef/d4/efd4940e84328c5a0637fe563406e04c28d1f9e1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.46300/9106.2021.15.8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

An Introduction to Trajectory Optimization: How to Do Your Own Direct Collocation

Matthew Kelly
<span title="">2017</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ptdzvkiimng2hoib3gq2mgqyi4" style="color: black;">SIAM Review</a> </i> &nbsp;
This is because trapezoidal collocation approximates the objective function and system dynamics as piece-wise linear functions, while Hermite-Simpson collocation approximates them as piece-wise quadratic  ...  Trapezoidal collocation works by approximating the control trajectory and the system dynamics as piece-wise linear functions, also known as a linear splines, shown in Figure 3 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/16m1062569">doi:10.1137/16m1062569</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/q6llm5sg3bhzhl2whz5y5gqe4a">fatcat:q6llm5sg3bhzhl2whz5y5gqe4a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190304074729/http://pdfs.semanticscholar.org/ba1f/38d6bbbf7227cda93f3915bc3fa7fc37b58e.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ba/1f/ba1f38d6bbbf7227cda93f3915bc3fa7fc37b58e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/16m1062569"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Cascade-Forward Neural Network for Volterra Integral Equation Solution

Shymaa Akram Hantoush Alrubaie
<span title="2021-08-01">2021</span> <i title="College of Education for Pure Sciences Ibn Al-Haitham"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/l6aasw5e7vgfdaese5t6vnjy7e" style="color: black;">Ibn AL- Haitham Journal For Pure and Applied Science</a> </i> &nbsp;
output of this network.  ...  The importance of this equation appeares new direction to solve the equation by using new methods to avoid obstacles. One of these methods employ neural network for obtaining the solution.  ...  [10] develop numerical collocation method depending on approximate of the exact solution of superposition of sigmoidal functions to solve linear and nonlinear VIE of the second kind, the algorithm is  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.30526/34.3.2683">doi:10.30526/34.3.2683</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rng3zeyrzbhsnfcfdjfti7itvy">fatcat:rng3zeyrzbhsnfcfdjfti7itvy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210811232126/https://jih.uobaghdad.edu.iq/index.php/j/article/download/2683/1695" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7c/29/7c29d3681b1e33567d58a8f26d67332b09257009.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.30526/34.3.2683"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Discrete signals, feedback and oscillation

Yoshifumi Okuyama
<span title="">2014</span> <i title="IEEE"> 2014 IEEE Conference on Norbert Wiener in the 21st Century (21CW) </i> &nbsp;
The stability condition of (nonlinear) discrete systems is derived by using the extended small-gain-theorem with an arbitrary number .  ...  In numerical examples, some discrete time-responses and chaotic oscillations are shown in relation to the size of sampling-period and the magnitude of step-input.  ...  This sector agrees approximately with the above area as shown in Fig. 8 .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/norbert.2014.6893910">doi:10.1109/norbert.2014.6893910</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nenye6eribdpxf4eiisnhhugmu">fatcat:nenye6eribdpxf4eiisnhhugmu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150220153538/http://humanitech-lab.jp/pdfs/Wiener12.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/18/a9/18a964291d670c57a411c59e510d2c68b5166d34.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/norbert.2014.6893910"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>
&laquo; Previous Showing results 1 &mdash; 15 out of 29,107 results