Relevant bibliographies by topics / Runge-Kutta metody

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  2. Dissertations / Theses
  3. Books
  4. Book chapters
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Academic literature on the topic 'Runge-Kutta metody'

Author: Grafiati
Published: 4 June 2021
Last updated: 17 February 2022

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Journal articles on the topic "Runge-Kutta metody"

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Jackiewicz, Zdzislaw, Rosemary Anne Renaut, and Marino Zennaro. "Explicit two-step Runge-Kutta methods." Applications of Mathematics 40, no. 6 (1995): 433–56. http://dx.doi.org/10.21136/am.1995.134306.

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Hidayat, Taufik, Jenizon ., and Budi Rudianto. "APLIKASI PRINSIP MAKSIMUM PONTRYAGIN DAN METODE RUNGE-KUTTA DALAM MASALAH KONTROL OPTIMAL." Jurnal Matematika UNAND 7, no. 2 (May 1, 2018): 212. http://dx.doi.org/10.25077/jmu.7.2.212-220.2018.

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Abstrak. Tulisan ini membahas tentang penggunaan prinsip maksimum pontryagin danmetode Runge-Kutta dalam masalah kontrol optimal. Prinsip maksimum pontryagin di-gunakan untuk menentukan solusi analitik, dan metode Runge-Kutta untuk menentukansolusi numerik. Hasil dari metode Runge-Kutta kemudian dibandingkan dengan solusianalitiknya. Dari hasil perbandingan dapat disimpulkan metode Runge-Kutta mem-berikan galat yang sangatlah kecil dan dapat diabaikan.Kata Kunci: Masalah Kontrol Optimal, Prinsip Maksimum Pontryagin, Runge-Kutta
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Segarra, Jaime. "MÉTODOS NUMÉRICOS RUNGE-KUTTA Y ADAMS BASHFORTH-MOULTON EN MATHEMATICA." Revista Ingeniería, Matemáticas y Ciencias de la Información 7, no. 14 (July 15, 2020): 13–32. http://dx.doi.org/10.21017/rimci.2020.v7.n14.a81.

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n este estudio, el objetivo principal es realizar el análisis de los métodos numéricos Runge-Kutta y Adams Bashforth-Moulton. Para cumplir con el objetivo se utilizó el sistema de ecuaciones diferenciales del modelo Lotka-Volterra y se usó el software matemático Wolfram Mathematica. En los resultados se realiza la comparación de los métodos RK4, AB4 y AM4 con el comando NDSolve utilizando el modelo Lotka-Volterra. Los resultados obtenidos en los diagramas de fase y la tabla de puntos de la iteración indicaron que el método RK4 tiene mayor precisión que los métodos AB4 y AM4.
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Acu, Yulia, Boni Pahlanop Lapanporo, and Arie Antasari Kushadiwijayanto. "Model Sederhana Gerak Osilator dengan Massa Berubah Terhadap Waktu Menggunakan Metode Runge Kutta." POSITRON 7, no. 2 (January 6, 2018): 42. http://dx.doi.org/10.26418/positron.v7i2.23276.

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Persamaan gerak osilasi pegas dengan massa berubah terhadap waktu merupakan persamaan differensial non linear yang sulit diselesaikan secara analitik. Pada penelitian ini persamaan gerak osilasi tersebut diselesaikan menggunakan metode Runge Kutta orde empat dan Runge Kutta Fehlberg tingkat lima. Metode Runge Kutta menawarkan penyelesaian persamaan diferensial dengan pertumbuhan truncation error yang jauh lebih kecil. Hasilnya menunjukan gerak osilator dengan massa yang terus berkurang terhadap waktu memiliki sifat seperti osilator teredam dan menjadi gerak harmonik sederhana saat massa osilator tetap. Metode Runge Kutta orde empat dan Runge Kutta Fehlberg mampu menggambarkan keadaan sistem osilator dengan massa berubah terhadap waktu.
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Rahmatullah, Sigid, Yudha Arman, and Apriansyah Apriansyah. "Simulasi Gerak Osilasi Model Pegas Bergandeng Menggunakan Metode Runge-Kutta." PRISMA FISIKA 8, no. 3 (December 15, 2020): 180. http://dx.doi.org/10.26418/pf.v8i3.43681.

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Persamaan gerak sistem pegas bergandeng Fay dan Graham (2003) telah diselesaikan secara numerik untuk kemudian dibandingkan dengan hasil perhitungan analitik. Nilai kesebandingan didasarkan pada Symmetric Mean Absolute Percentage Error (SMAPE). Metode numerik utama yang digunakan untuk menyelesaikan persamaan gerak model pegas bergandeng adalah Runge-Kutta Orde Empat dan Runge-Kutta 45 Fehlberg sedangkan metode Leapfrog dan Euler digunakan sebagai metode tambahan uji. Ukuran langkah h yang digunakan adalah 0,05 s. Berdasarkan hasil perhitungan dan nilai SMAPE yang diperoleh, Runge-Kutta 45 Fehlberg menjadi metode numerik dengan tingkat ketelitian yang paling baik diantara berbagai metode numerik yang digunakan pada konfigurasi sistem pegas hasil modifikasi model Fay dan Graham (2003) dengan variasi massa m, arah simpangan x, dan besar konstanta pegas k.Kata Kunci : Pegas, Runge Kutta 45 Fehlberg
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Hurit, Roberta Uron, and Sudi Mungkasi. "The Euler, Heun, and Fourth Order Runge-Kutta Solutions to SEIR Model for the Spread of Meningitis Disease." Mathline : Jurnal Matematika dan Pendidikan Matematika 6, no. 2 (August 2, 2021): 140–53. http://dx.doi.org/10.31943/mathline.v6i2.176.

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Penelitian ini bertujuan untuk menyelesaikan model SEIR penyebaran penyakit meningitis menggunakan metode Euler, metode Heun dan metode Runge-Kutta orde empat, dimana model persamaannya berupa persamaan diferensial nonlinear. Metode penelitian yang digunakan adalah pemrograman komputer dan simulasi. Dari simulasi, ketiga metode tersebut menghasilkan penyelesaian dengan perilaku yang mirip, yaitu semua gambar grafik pada setiap simulasi mempunyai bentuk pola yang sama. Hal ini memberikan kepercayaan pada kebenaran hasil simulasi dalam makalah ini. Secara teori, metode Runge-Kutta orde empat memiliki ketelitian yang lebih tinggi dibandingkan dengan metode Euler dan metode Heun. Kata Kunci: penyebaran penyakit meningitis, model SEIR, metode Euler, metode Heun, metode Runge-Kutta orde empat.
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Zheng, Zheming, and Linda Petzold. "Runge–Kutta–Chebyshev projection method." Journal of Computational Physics 219, no. 2 (December 2006): 976–91. http://dx.doi.org/10.1016/j.jcp.2006.07.005.

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Tan, Jia Bo. "Symplectic Partitioned Runge-Kutta and Symplectic Runge-Kutta Methods Generated by 2-Stage RadauIA Method." Applied Mechanics and Materials 444-445 (October 2013): 633–36. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.633.

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To preserve the symplecticity property, it is natural to require numerical integration of Hamiltonian systems to be symplectic. As a famous numerical integration, it is known that the 2-stage RadauIA method is not symplectic. With the help of symplectic conditions of Runge-Kutta method and partitioned Runge-Kutta method, a symplectic partitioned Runge-Kutta method and a symplectic Runge-Kutta method are constructed on the basis of 2-stage RadauIA method in this paper.
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Muhammad, Raihanatu. "THE ORDER AND ERROR CONSTANT OF A RUNGE-KUTTA TYPE METHOD FOR THE NUMERICAL SOLUTION OF INITIAL VALUE PROBLEM." FUDMA JOURNAL OF SCIENCES 4, no. 2 (October 13, 2020): 743–48. http://dx.doi.org/10.33003/fjs-2020-0402-256.

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Implicit Runge- Kutta methods are used for solving stiff problems which mostly arise in real life situations. Analysis of the order, error constant, consistency and convergence will help in determining an effective Runge- Kutta Method (RKM) to use. Due to the loss of linearity in Runge –Kutta Methods and the fact that the general Runge –Kutta Method makes no mention of the differential equation makes it impossible to define the order of the method independently of the differential equation. In this paper, we examine in simpler details how to obtain the order, error constant, consistency and convergence of a Runge -Kutta Type method (RKTM) when the step number .
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Suryani, Irma, Wartono Wartono, and Yuslenita Muda. "Modification of Fourth order Runge-Kutta Method for Kutta Form With Geometric Means." Kubik: Jurnal Publikasi Ilmiah Matematika 4, no. 2 (February 25, 2020): 221–30. http://dx.doi.org/10.15575/kubik.v4i2.6425.

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This paper discuss how to modified Fourth order Runge-Kutta Kutta method based on the geometric mean. Then we have parameters and however by re-comparing the Taylor series expansion of and up to the 4th order. For make error term re-compering of the Taylor series expansion of and up to the 5th order. In the error term an make substitution for the values of and into the Taylor seriese expansion up to the 5th order. So that we have error term modified Fourth Order Runge-Kutta Kutta based on the geometric mean. Modified Fourth Order Runge-Kutta Kutta based on the geometric mean that usually used to solved ordinary differential equations.
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Dissertations / Theses on the topic "Runge-Kutta metody"

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Kroulíková, Tereza. "Runge-Kuttovy metody." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2018. http://www.nusl.cz/ntk/nusl-392847.

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Tato práce se zabývá Runge--Kuttovými metodami pro počáteční problém. Práce začíná analýzou Eulerovy metody a odvozením podmínek řádu. Jsou představeny modifikované metody. Pro dvě z nich je určen jejich řád teoreticky a pro všechny je provedeno numerické testování řádu. Jsou představeny a numericky testovány dva typy metod s odhadem chyby, "embedded" metody a metody založené na modifikovaných metodách. V druhé části jsou odvozeny implicitní metody. Jsou představeny dva způsoby konstrukce implicitních "embedded" metod. Jsou zmíněny také diagonální implicitní metody. Na závěr jsou probrány dva druhy stability u metod prezentovaných v práci.
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Sehnalová, Pavla. "Stabilita a konvergence numerických výpočtů." Doctoral thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2011. http://www.nusl.cz/ntk/nusl-261248.

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Tato disertační práce se zabývá analýzou stability a konvergence klasických numerických metod pro řešení obyčejných diferenciálních rovnic. Jsou představeny klasické jednokrokové metody, jako je Eulerova metoda, Runge-Kuttovy metody a nepříliš známá, ale rychlá a přesná metoda Taylorovy řady. V práci uvažujeme zobecnění jednokrokových metod do vícekrokových metod, jako jsou Adamsovy metody, a jejich implementaci ve dvojicích prediktor-korektor. Dále uvádíme generalizaci do vícekrokových metod vyšších derivací, jako jsou např. Obreshkovovy metody. Dvojice prediktor-korektor jsou často implementovány v kombinacích modů, v práci uvažujeme tzv. módy PEC a PECE. Hlavním cílem a přínosem této práce je nová metoda čtvrtého řádu, která se skládá z dvoukrokového prediktoru a jednokrokového korektoru, jejichž formule využívají druhých derivací. V práci je diskutována Nordsieckova reprezentace, algoritmus pro výběr proměnlivého integračního kroku nebo odhad lokálních a globálních chyb. Navržený přístup je vhodně upraven pro použití proměnlivého integračního kroku s přístupe vyšších derivací. Uvádíme srovnání s klasickými metodami a provedené experimenty pro lineární a nelineární problémy.
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Elmikkawy, M. E. A. "Embedded Runge-Kutta-Nystrom methods." Thesis, Teesside University, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.371400.

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Macdougall, Thomas Anthony. "Global error estimators for explicit Runge-Kutta methods." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0001/MQ28227.pdf.

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Tanner, Gregory Mark. "Generalized additive Runge-Kutta methods for stiff odes." Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/6507.

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In many applications, ordinary differential equations can be additively partitioned \[y'=f(y)=\sum_{m=1}^{N}\f{}{m}(y).] It can be advantageous to discriminate between the different parts of the right-hand side according to stiffness, nonlinearity, evaluation cost, etc. In 2015, Sandu and G\"{u}nther \cite{sandu2015gark} introduced Generalized Additive Runge-Kutta (GARK) methods which are given by \begin{eqnarray*} Y_{i}^{\{q\}} & = & y_{n}+h\sum_{m=1}^{N}\sum_{j=1}^{s^{\{m\}}}a_{i,j}^{\{q,m\}}f^{\{m\}}\left(Y_{j}^{\{m\}}\right)\\ & & \text{for } i=1,\dots,s^{\{q\}},\,q=1,\dots,N\\ y_{n+1} & = & y_{n}+h\sum_{m=1}^{N}\sum_{j=1}^{s^{\{m\}}}b_{j}^{\{m\}}f^{\{m\}}\left(Y_{j}^{\{m\}}\right)\end{eqnarray*} with the corresponding generalized Butcher tableau \[\begin{array}{c|ccc} \c{}{1} & \A{1,1} & \cdots & \A{1,N}\\\vdots & \vdots & \ddots & \vdots\\ \c{}{N} & \A{N,1} & \cdots & \A{N,N}\\\hline & \b{}{1} & \cdots & \b{}{N}\end{array}\] The diagonal blocks $\left(\A{q,q},\b{}{q},\c{}{q}\right)$ can be chosen for example from standard Runge-Kutta methods, and the off-diagonal blocks $\A{q,m},\:q\neq m,$ act as coupling coefficients between the underlying methods. The case when $N=2$ and both diagonal blocks are implicit methods (IMIM) is examined. This thesis presents order conditions and simplifying assumptions that can be used to choose the off-diagonal coupling blocks for IMIM methods. Error analysis is performed for stiff problems of the form \begin{eqnarray*}\dot{y} & = & f(y,z)\\ \epsilon\dot{z} & = & g(y,z)\end{eqnarray*} with small stiffness parameter $\epsilon.$ As $\epsilon\to 0,$ the problem reduces to an index 1 differential algebraic equation provided $g_{z}(y,z)$ is invertible in a neighborhood of the solution. A tree theory is developed for IMIM methods applied to the reduced problem. Numerical results will be presented for several IMIM methods applied to the Van der Pol equation.
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Ijaz, Muhammad. "Implicit runge-kutta methods to simulate unsteady incompressible flows." Texas A&M University, 2007. http://hdl.handle.net/1969.1/85850.

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A numerical method (SIMPLE DIRK Method) for unsteady incompressible viscous flow simulation is presented. The proposed method can be used to achieve arbitrarily high order of accuracy in time-discretization which is otherwise limited to second order in majority of the currently used simulation techniques. A special class of implicit Runge-Kutta methods is used for time discretization in conjunction with finite volume based SIMPLE algorithm. The algorithm was tested by solving for velocity field in a lid-driven square cavity. In the test case calculations, power law scheme was used in spatial discretization and time discretization was performed using a second-order implicit Runge-Kutta method. Time evolution of velocity profile along the cavity centerline was obtained from the proposed method and compared with that obtained from a commercial computational fluid dynamics software program, FLUENT 6.2.16. Also, steady state solution from the present method was compared with the numerical solution of Ghia, Ghia, and Shin and that of Erturk, Corke, and Goökçöl. Good agreement of the solution of the proposed method with the solutions of FLUENT; Ghia, Ghia, and Shin; and Erturk, Corke, and Goökçöl establishes the feasibility of the proposed method.
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Fletcher, Matthew T. "Discovery and optimization of low-storage Runge-Kutta methods." Thesis, Monterey, California: Naval Postgraduate School, 2015. http://hdl.handle.net/10945/45852.

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Runge-Kutta (RK) methods are an important family of iterative methods for approximating the solutions of ordinary differential equations (ODEs) and differential algebraic equations (DAEs). It is common to use an RK method to discretize in time when solving time dependent partial differential equations (PDEs) with a method-of-lines approach as in Maxwell’s Equations. Different types of PDEs are discretized in such a way that could result in a high dimensional ODE or DAE.We use a low-storage RK (LSRK) method that stores two registers per ODE dimension, which limits the impact of increased storage requirements. Classical RK methods, however, have one storage variable per stage. In this thesis we compare the efficiency and accuracy of LSRK methods to RK methods. We then focus on optimizing the truncation error coefficients for LSRK to discover new methods. Reusing the tools from the optimization method, we discover new methods for low-storage half-explicit RK (LSHERK) methods for solving DAEs.
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Lui, Ho Man. "Runge-Kutta Discontinuous Galerkin method for the Boltzmann equation." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/39215.

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Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006.
Includes bibliographical references (p. 85-87).
In this thesis we investigate the ability of the Runge-Kutta Discontinuous Galerkin (RKDG) method to provide accurate and efficient solutions of the Boltzmann equation. Solutions of the Boltzmann equation are desirable in connection to small scale science and technology because when characteristic flow length scales become of the order of, or smaller than, the molecular mean free path, the Navier-Stokes description fails. The prevalent Boltzmann solution method is a stochastic particle simulation scheme known as Direct Simulation Monte Carlo (DSMC). Unfortunately, DSMC is not very effective in low speed flows (typical of small scale devices of interest) because of the high statistical uncertainty associated with the statistical sampling of macroscopic quantities employed by this method. This work complements the recent development of an efficient low noise method for calculating the collision integral of the Boltzmann equation, by providing a high-order discretization method for the advection operator balancing the collision integral in the Boltzmann equation. One of the most attractive features of the RKDG method is its ability to combine high-order accuracy, both in physical space and time, with the ability to capture discontinuous solutions.
(cont.) The validity of this claim is thoroughly investigated in this thesis. It is shown that, for a model collisionless Boltzmann equation, high-order accuracy can be achieved for continuous solutions; whereas for discontinuous solutions, the RKDG method, with or without the application of a slope limiter such as a viscosity limiter, displays high-order accuracy away from the vicinity of the discontinuity. Given these results, we developed a RKDG solution method for the Boltzmann equation by formulating the collision integral as a source term in the advection equation. Solutions of the Boltzmann equation, in the form of mean velocity and shear stress, are obtained for a number of characteristic flow length scales and compared to DSMC solutions. With a small number of elements and a low order of approximation in physical space, the RKDG method achieves similar results to the DSMC method. When the characteristic flow length scale is small compared to the mean free path (i.e. when the effect of collisions is small), oscillations are present in the mean velocity and shear stress profiles when a coarse velocity space discretization is used. With a finer velocity space discretization, the oscillations are reduced, but the method becomes approximately five times more computationally expensive.
(cont.) We show that these oscillations (due to the presence of propagating discontinuities in the distribution function) can be removed using a viscosity limiter at significantly smaller computational cost.
by Ho Man Lui.
S.M.
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Fenton, P. "The dynamics of variable time-stepping Runge-Kutta methods." Thesis, University of Sussex, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.394994.

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Ramos, Manoel Wallace Alves. "Métodos de Euler e Runge-Kutta: uma análise utilizando o Geogebra." Universidade Federal da Paraíba, 2017. http://tede.biblioteca.ufpb.br:8080/handle/tede/9381.

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Is evident the importance of ordinary differential equations in modeling problems in several areas of science. Coupled with this, is increasing the use of numerical methods to solve such equations. Computers have become an extremely useful tool in the study of differential equations, since through them it is possible to execute algorithms that construct numerical approximations for solutions of these equati- ons. This work introduces the study of numerical methods for ordinary differential equations presenting the numerical Eulerºs method, improved Eulerºs method and the class of Runge-Kuttaºs methods. In addition, in order to collaborate with the teaching and learning of such methods, we propose and show the construction of an applet created from the use of Geogebm software tools. The applet provides approximate numerical solutions to an initial value problem, as well as displays the graphs of the solutions that are obtained from the numerical Eulerºs method, im- proved Eulerºs method, and fourth-order Runge-Kuttaºs method.
É evidente a importancia das equações diferenciais ordinarias na modelagem de problemas em diversas áreas da ciência, bem como o uso de métodos numéricos para resolver tais equações. Os computadores são uma ferramenta extremamente útil no estudo de equações diferenciais, uma vez que através deles é possível executar algo- ritmos que constroem aproximações numéricas para soluções destas equações. Este trabalho é uma introdução ao estudo de métodos numéricos para equações diferen- ciais ordinarias. Apresentamos os métodos numéricos de Euler, Euler melhorado e a classe de métodos de Runge-Kutta. Além disso, com o propósito de colaborar com o ensino e aprendizagem de tais métodos, propomos e mostramos a construção de um applet criado a partir do uso de ferramentas do software Geogebra. O applet fornece soluções numéricas aproximadas para um problema de valor inicial, bem como eXibe os graficos das soluções que são obtidas a partir dos métodos numéricos de Euler, Euler melhorado e Runge-Kutta de quarta ordem.
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Books on the topic "Runge-Kutta metody"

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Gottlieb, Sigal. Total variation diminishing Runge-Kutta schemes. Hampton, VA: National Aerospace and Space Administration, Langley Research Center, 1996.

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Keeling, Stephen L. On implicit Runge-Kutta methods for parallel computations. Hampton, Va: ICASE, 1987.

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Carpenter, Mark H. Fourth-order 2N-storage Runge-Kutta schemes. Hampton, Va: Langley Research Center, 1994.

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Keeling, Stephen L. Galerkin/Runge-Kutta discretizations for semilinear parabolic equations. Hampton, Va: ICASE, 1987.

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Zingg, D. W. Runge-Kutta methods for linear ordinary differential equations. [Moffett Field, Calif.]: Research Institute for Advanced Computer Science, NASA Ames Research Center, 1997.

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Enenkel, Robert Frederick. Implementation of parallel predictor-corrector Runge-Kutta methods. Toronto: University of Toronto, Dept. of Computer Science, 1988.

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Zingg, D. W. Runge-Kutta methods for linear ordinary differential equations. [Moffett Field, Calif.]: Research Institute for Advanced Computer Science, NASA Ames Research Center, 1997.

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Zingg, D. W. Runge-Kutta methods for linear ordinary differential equations. [Moffett Field, Calif.]: Research Institute for Advanced Computer Science, NASA Ames Research Center, 1997.

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Zingg, D. W. Runge-Kutta methods for linear ordinary differential equations. [Moffett Field, Calif.]: Research Institute for Advanced Computer Science, NASA Ames Research Center, 1997.

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Merkle, Charles L. Application of Runge-Kutta schemes to incompressible flows. New York: American Institute of Aeronautics and Astronautics, 1986.

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Book chapters on the topic "Runge-Kutta metody"

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Agarwal, Ravi P., Simona Hodis, and Donal O’Regan. "Runge–Kutta Method." In 500 Examples and Problems of Applied Differential Equations, 163–82. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-26384-3_6.

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Palais, Richard, and Robert Palais. "Runge-Kutta Methods." In The Student Mathematical Library, 263–79. Providence, Rhode Island: American Mathematical Society, 2009. http://dx.doi.org/10.1090/stml/051/14.

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Feng, Kang, and Mengzhao Qin. "Symplectic Runge-Kutta Methods." In Symplectic Geometric Algorithms for Hamiltonian Systems, 277–364. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-01777-3_8.

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Abdulle, Assyr. "Explicit Stabilized Runge–Kutta Methods." In Encyclopedia of Applied and Computational Mathematics, 460–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_100.

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Hairer, Ernst, and Gerhard Wanner. "Runge–Kutta Methods, Explicit, Implicit." In Encyclopedia of Applied and Computational Mathematics, 1282–85. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_144.

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Razali, N., and R. P. K. Chan. "Symmetrizers for Runge–Kutta Methods." In International Conference on Mathematical Sciences and Statistics 2013, 195–203. Singapore: Springer Singapore, 2014. http://dx.doi.org/10.1007/978-981-4585-33-0_20.

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Hundsdorfer, Willem, and Jan Verwer. "Stabilized Explicit Runge-Kutta Methods." In Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, 419–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-09017-6_5.

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Hairer, Ernst, Syvert Paul Nørsett, and Gerhard Wanner. "Runge-Kutta and Extrapolation Methods." In Solving Ordinary Differential Equations I, 127–301. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-662-12607-3_2.

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Nørsett, Syvert P., and Harald H. Simonsen. "Aspects of parallel Runge-Kutta methods." In Numerical Methods for Ordinary Differential Equations, 103–17. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0089234.

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Hairer, Ernst, and Gerhard Wanner. "Construction of Implicit Runge-Kutta Methods." In Springer Series in Computational Mathematics, 71–90. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-05221-7_5.

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Conference papers on the topic "Runge-Kutta metody"

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Monovasilis, Th, Z. Kalogiratou, and T. E. Simos. "Exponentially fitted symplectic Runge-Kutta-Nyström methods derived by partitioned Runge-Kutta methods." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825720.

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Monovasilis, Theodore, Zacharoula Kalogiratou, and T. E. Simos. "Construction of exponentially fitted symplectic Runge-Kutta-Nyström methods from partitioned Runge-Kutta methods." In INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2014 (ICCMSE 2014). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4897864.

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Voss, D. A. "Factored two-step Runge-Kutta methods." In the conference. New York, New York, USA: ACM Press, 1989. http://dx.doi.org/10.1145/101007.101043.

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Zingg, D., and T. Chisholm. "Runge-Kutta methods for linear problems." In 12th Computational Fluid Dynamics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1995. http://dx.doi.org/10.2514/6.1995-1756.

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Eremin, Alexey. "Functional continuous Runge–Kutta–Nyström methods." In The 10'th Colloquium on the Qualitative Theory of Differential Equations. Szeged: Bolyai Institute, SZTE, 2016. http://dx.doi.org/10.14232/ejqtde.2016.8.11.

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Karim, Samsul Ariffin Abdul, Mohd Tahir Ismail, Mohammad Khatim Hasan, and Jumat Sulaiman. "Data interpolation using Runge Kutta method." In PROCEEDING OF THE 25TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM25): Mathematical Sciences as the Core of Intellectual Excellence. Author(s), 2018. http://dx.doi.org/10.1063/1.5041644.

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Monovasilis, Th, Z. Kalogiratou, and T. E. Simos. "Comparison of two derivative Runge Kutta methods." In INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2018 (ICCMSE 2018). Author(s), 2018. http://dx.doi.org/10.1063/1.5079222.

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You, Xiong, Xinmeng Yao, and Xin Shu. "An Optimized Fourth Order Runge-Kutta Method." In 2010 Third International Conference on Information and Computing Science (ICIC). IEEE, 2010. http://dx.doi.org/10.1109/icic.2010.195.

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Aristoff, Jeffrey, and Aubrey Poore. "Implicit Runge-Kutta Methods for Orbit Propagation." In AIAA/AAS Astrodynamics Specialist Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2012. http://dx.doi.org/10.2514/6.2012-4880.

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Monovasilis, Th, Z. Kalogiratou, and T. E. Simos. "Exponentially fitted symplectic Runge-Kutta-Nyström methods." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756418.

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Reports on the topic "Runge-Kutta metody"

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Tang, Hai C. Parallelizing a fourth-order Runge-Kutta method. Gaithersburg, MD: National Institute of Standards and Technology, 1997. http://dx.doi.org/10.6028/nist.ir.6031.

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