Relevant bibliographies by topics / Runge-Kutta Method

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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 'Runge-Kutta Method'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 April 2022

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Journal articles on the topic "Runge-Kutta Method"

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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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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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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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Sundaram, Arunachalam. "Application of Runge – Kutta Method to Population Equations." International Journal for Research in Applied Science and Engineering Technology 10, no. 4 (April 30, 2022): 719–24. http://dx.doi.org/10.22214/ijraset.2022.41358.

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Abstract: In this paper, we implement the second order Runge – Kutta method for three different population initial value problems. The Runge – Kutta method is a numerical technique used to solve the approximate solution for initial value problems for ordinary differential equations. Runge – Kutta method is implemented to linear population equation, non-linear population equation and non-linear population equation with an oscillation. The method of solving three initial value problems is implemented using Python Programming. Keywords: Differential equation, Runge – Kutta method, Discrete interval, Population equation, Non-linear population equation, Oscillation, Python.
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Liu, M. Y., L. Zhang, and C. F. Zhang. "Study on Banded Implicit Runge–Kutta Methods for Solving Stiff Differential Equations." Mathematical Problems in Engineering 2019 (October 10, 2019): 1–8. http://dx.doi.org/10.1155/2019/4850872.

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The implicit Runge–Kutta method with A-stability is suitable for solving stiff differential equations. However, the fully implicit Runge–Kutta method is very expensive in solving large system problems. Although some implicit Runge–Kutta methods can reduce the cost of computation, their accuracy and stability are also adversely affected. Therefore, an effective banded implicit Runge–Kutta method with high accuracy and high stability is proposed, which reduces the computation cost by changing the Jacobian matrix from a full coefficient matrix to a banded matrix. Numerical solutions and results of stiff equations obtained by the methods involved are compared, and the results show that the banded implicit Runge–Kutta method is advantageous to solve large stiff problems and conducive to the development of simulation.
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Qudsi, Rahma, and Agus Dahlia. "BEBERAPA KOMBINASI RUNGE-KUTTA UNTUK MENENTUKAN SOLUSI PERSAMAAN DIFERENSIAL WAKTU TUNDA." JURNAL MATEMATIKA MURNI DAN TERAPAN EPSILON 13, no. 1 (June 1, 2019): 13. http://dx.doi.org/10.20527/epsilon.v13i1.1243.

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Delay Differential Equation (DDE) have been applied to many area. While, we rarely get the analytic solutions of DDE. Many researchers have found many methods to find it for instance Runge-Kutta Method. The purpose of this paper is to accumulate the combinations of Runge-Kutta method which is used to find the solutions of DDE. Keywords : Delay Differential Equation, Interpolation, Runge-Kutta Method
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Chauhan, Vijeyata, and Pankaj Kumar Srivastava. "Computational Techniques Based on Runge-Kutta Method of Various Order and Type for Solving Differential Equations." International Journal of Mathematical, Engineering and Management Sciences 4, no. 2 (April 1, 2019): 375–86. http://dx.doi.org/10.33889/ijmems.2019.4.2-030.

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The Runge-Kutta method is a one step method with multiple stages, the number of stages determine order of method. The method can be applied to work out on differential equation of the type’s explicit, implicit, partial and delay differential equation etc. The present paper describes a review on recent computational techniques for solving differential equations using Runge-Kutta algorithm of various order. This survey includes the summary of the articles of last decade till recent years based on third; fourth; fifth and sixth order Runge-Kutta methods. Along with this a combination of these methods and various other type of Runge-Kutta algorithm based articles are included. Comparisons of methods with own critical comments as remarks have been included.
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Rabiei, Faranak, Fatin Abd Hamid, Nafsiah Md Lazim, Fudziah Ismail, and Zanariah Abdul Majid. "Numerical Solution of Volterra Integro-Differential Equations Using Improved Runge-Kutta Methods." Applied Mechanics and Materials 892 (June 2019): 193–99. http://dx.doi.org/10.4028/www.scientific.net/amm.892.193.

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In this paper, we proposed the numerical solution of Volterra integro-differential equations of the second kind using Improved Runge-Kutta method of order three and four with 2 stages and 4 stages, respectively. The improved Runge-kutta method is considered as two-step numerical method for solving the ordinary differential equation part and the integral operator in Volterra integro-differential equation is approximated using quadrature rule and Lagrange interpolation polynomials. To illustrate the efficiency of proposed methods, the test problems are carried out and the numerical results are compared with existing third and fourth order classical Runge-Kutta method with 3 and 4 stages, respectively. The numerical results showed that the Improved Runge-Kutta method by achieving the higher accuracy performed better results than existing methods.
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Lobão, Diomar Cesar. "Low storage explicit Runge-Kutta method." Semina: Ciências Exatas e Tecnológicas 40, no. 2 (December 18, 2019): 123. http://dx.doi.org/10.5433/1679-0375.2019v40n2p123.

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Neste artigo estamos tratando dos métodos explícitos Runge Kutta (LSERK) de alta ordem e baixo armazenamento, que são usados principalmente para a discretização temporal e são estáveis independentemente de sua precisão. O principal objetivo deste trabalho é comparar o RK tradicional com diferentes formas de métodos LSERK. Os experimentos numéricos indicam que tais métodos são altamente precisos e eficazes para propósitos numéricos. Também é mostrado o tempo de CPU e suas implicações na solução. O método é bem adequado para obter uma solução precisa de alta ordem para o problema escalar de segunda ordem do problema de valor inicial (IVP), como é discutido no presente artigo.
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Tiwari, Shruti, and Ram K. Pandey. "Exponentially-fitted pseudo Runge-Kutta method." International Journal of Computing Science and Mathematics 12, no. 2 (2020): 105. http://dx.doi.org/10.1504/ijcsm.2020.10033205.

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Dissertations / Theses on the topic "Runge-Kutta Method"

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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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Auffredic, Jérémy. "A second order Runge–Kutta method for the Gatheral model." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-49170.

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In this thesis, our research focus on a weak second order stochastic Runge–Kutta method applied to a system of stochastic differential equations known as the Gatheral Model. We approximate numerical solutions to this system and investigate the rate of convergence of our method. Both call and put options are priced using Monte-Carlo simulation to investigate the order of convergence. The numerical results show that our method is consistent with the theoretical order of convergence of the Monte-Carlo simulation. However, in terms of the Runge-Kutta method, we cannot accept the consistency of our method with the theoretical order of convergence without further research.
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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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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
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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Saleh, Ali, and Ahmad Al-Kadri. "Option pricing under Black-Scholes model using stochastic Runge-Kutta method." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-53783.

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The purpose of this paper is solving the European option pricing problem under the Black–Scholes model. Our approach is to use the so-called stochastic Runge–Kutta (SRK) numericalscheme to find the corresponding expectation of the functional to the stochastic differentialequation under the Black–Scholes model. Several numerical solutions were made to study howquickly the result converges to the theoretical value. Then, we study the order of convergenceof the SRK method with the help of MATLAB.
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Edgar, Christopher A. "An adaptive Runge-Kutta-Fehlberg method for time-dependent discrete ordinate transport." Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/53935.

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This dissertation focuses on the development and implementation of a new method to solve the time-dependent form of the linear Boltzmann transport equation for reactor transients. This new method allows for a stable solution to the fully explicit form of the transport equation with delayed neutrons by employing an error-controlled, adaptive Runge-Kutta-Fehlberg (RKF) method to differentiate the time domain. Allowing for the time step size to vary adaptively and as needed to resolve the time-dependent behavior of the angular flux and neutron precursor concentrations. The RKF expansion of the time domain occurs at each point and is coupled with a Source Iteration to resolve the spatial behavior of the angular flux at the specified point in time. The decoupling of the space and time domains requires the application of a quasi-static iteration between solving the time domain using adaptive RKF with error control and resolving the space domain with a Source Iteration sweep. The research culminated with the development of the 1-D Adaptive Runge-Kutta Time-Dependent Transport code (ARKTRAN-TD), which successfully implemented the new method and applied it to a suite of reactor transient benchmarks.
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Booth, Andrew S. "Collocation methods for a class of second order initial value problems with oscillatory solutions." Thesis, Durham University, 1993. http://etheses.dur.ac.uk/5664/.

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We derive and analyse two families of multistep collocation methods for periodic initial-value problems of the form y" = f(x, y); y((^x)o) = yo, y(^1)(xo) = zo involving ordinary differential equations of second order in which the first derivative does not appear explicitly. A survey of recent results and proposed numerical methods is given in chapter 2. Chapter 3 is devoted to the analysis of a family of implicit Chebyshev methods proposed by Panovsky k Richardson. We show that for each non-negative integer r, there are two methods of order 2r from this family which possess non-vanishing intervals of periodicity. The equivalence of these methods with one-step collocation methods is also established, and these methods are shown to be neither P-stable nor symplectic. In chapters 4 and 5, two families of multistep collocation methods are derived, and their order and stability properties are investigated. A detailed analysis of the two-step symmetric methods from each class is also given. The multistep Runge-Kutta-Nystrom methods of chapter 4 are found to be difficult to analyse, and the specific examples considered are found to perform poorly in the areas of both accuracy and stability. By contrast, the two-step symmetric hybrid methods of chapter 5 are shown to have excellent stability properties, in particular we show that all two-step 27V-point methods of this type possess non-vanishing intervals of periodicity, and we give conditions under which these methods are almost P-stable. P-stable and efficient methods from this family are obtained and demonstrated in numerical experiments. A simple, cheap and effective error estimator for these methods is also given.
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Zamri, Mohd Y. "An improved treatment of two-dimensional two-phase flows of steam by a Runge-Kutta method." Thesis, University of Birmingham, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.251270.

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Mayo, Colin F. "Implementation of the Runge-Kutta-Fehlberg method for solution of ordinary differential equations on a parallel processor." Thesis, Monterey, California. Naval Postgraduate School, 1987. http://hdl.handle.net/10945/22285.

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Malroy, Eric Thomas. "Solution of the ideal adiabatic stirling model with coupled first order differential equations by the Pasic method." Ohio : Ohio University, 1998. http://www.ohiolink.edu/etd/view.cgi?ohiou1176410606.

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Boat, Matthew. "The time-domain numerical solution of Maxwell's electromagnetic equations, via the fourth order Runge-Kutta discontinuous Galerkin method." Thesis, Swansea University, 2008. https://cronfa.swan.ac.uk/Record/cronfa42532.

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This thesis presents a high-order numerical method for the Time-Domain solution of Maxwell's Electromagnetic equations in both one- and two-dimensional space. The thesis discuses the validity of high-order representation and improved boundary representation. The majority of the theory is concerned with the formulation of a high-order scheme which is capable of providing a numerical solution for specific two-dimensional scattering problems. Specifics of the theory involve the selection of a suitable numerical flux, the choice of appropriate boundary conditions, mapping between coordinate systems and basis functions. The effectiveness of the method is then demonstrated through a series of examples.
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Books on the topic "Runge-Kutta Method"

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

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

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

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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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Cockburn, B. Runge-Kutta discontinuous Galerkin methods for convection-dominated problems. Hampton, VA: ICASE, NASA Langley Research Center, 2000.

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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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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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Book chapters on the topic "Runge-Kutta Method"

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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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Griffiths, David F., and Desmond J. Higham. "Runge–Kutta Method—I: Order Conditions." In Numerical Methods for Ordinary Differential Equations, 123–34. London: Springer London, 2010. http://dx.doi.org/10.1007/978-0-85729-148-6_9.

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Bellen, A. "A Runge-Kutta-Nystrom Method for Delay Differential Equations." In Numerical Boundary Value ODEs, 271–83. Boston, MA: Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4612-5160-6_16.

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Ariffin, Noor Amalina Nisa, Norhayati Rosli, and Abdul Rahman Mohd Kasim. "Stability Analysis of 4-Stage Stochastic Runge-Kutta Method (SRK4) and Specific Stochastic Runge-Kutta Method (SRKS1.5) for Stochastic Differential Equations." In Proceedings of the Third International Conference on Computing, Mathematics and Statistics (iCMS2017), 187–94. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-7279-7_23.

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Boretti, A. A. "An explicit Runge-Kutta method for turbulent reacting flows calculations." In Numerical Combustion, 199–210. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-51968-8_84.

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Arora, Geeta, Varun Joshi, and Isa Sani Garki. "Developments in Runge–Kutta Method to Solve Ordinary Differential Equations." In Recent Advances in Mathematics for Engineering, 193–202. Title: Recent advances in mathematics for engineering / edited by Mangey Ram. Description: Boca Raton, FL : CRC Press, Taylor & Francis Group, [2020] | Series: Mathematical engineering, manufacturing, and management sciences: CRC Press, 2020. http://dx.doi.org/10.1201/9780429200304-9.

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Liu, Chunfeng, Haiming Wu, Li Feng, and Aimin Yang. "Parallel Fourth-Order Runge-Kutta Method to Solve Differential Equations." In Information Computing and Applications, 192–99. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-25255-6_25.

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Perrier, Vincent, and Erwin Franquet. "Runge–Kutta Discontinuous Galerkin Method for Multi–phase Compressible Flows." In Computational Fluid Dynamics 2010, 73–79. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-17884-9_7.

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Ben Amma, Bouchra, Said Melliani, and Lalla Saadia Chadli. "Numerical Solution of Intuitionistic Fuzzy Differential Equations by Runge–Kutta Verner Method." In Recent Advances in Intuitionistic Fuzzy Logic Systems and Mathematics, 53–69. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53929-0_5.

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Eremin, Alexey S., Nikolai A. Kovrizhnykh, and Igor V. Olemskoy. "Economical Sixth Order Runge–Kutta Method for Systems of Ordinary Differential Equations." In Computational Science and Its Applications – ICCSA 2019, 89–102. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-24289-3_8.

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Conference papers on the topic "Runge-Kutta Method"

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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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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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Gobithaasan, R. U., T. Y. Meng, A. R. M. Piah, and K. T. Miura. "Rendering log aesthetic curves via Runge-Kutta method." 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/10.1063/1.4887609.

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Monovasilis, Th, Z. Kalogiratou, T. E. Simos, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "A Trigonometrically Fitted Symplectic Runge-Kutta-Nyström Method." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637002.

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JORGENSON, PHILIP, and RODRICK CHIMA. "An unconditionally stable Runge-Kutta method for unsteady flows." In 27th Aerospace Sciences Meeting. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1989. http://dx.doi.org/10.2514/6.1989-205.

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Mohammadi, Sahryar, and Saeede Zare Hosseini. "Virtual Password Using Runge-Kutta Method for Internet Banking." In 2010 Second International Conference on Communication Software and Networks. IEEE, 2010. http://dx.doi.org/10.1109/iccsn.2010.118.

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Syai'in, Mat, and Kuo Lung Lian. "Microgrid power flow using Homotopic and Runge-Kutta Method." In 2015 IEEE 2nd International Future Energy Electronics Conference (IFEEC). IEEE, 2015. http://dx.doi.org/10.1109/ifeec.2015.7361462.

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Tan, Jiabo. "A New Symplectic Runge-Kutta Method of 3 Order." In 2013 Fifth International Conference on Computational and Information Sciences (ICCIS). IEEE, 2013. http://dx.doi.org/10.1109/iccis.2013.250.

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Xinrong Hu and Lan Wei. "A modified embedded Runge-Kutta method for cloth simulation." In China-Ireland International Conference on Information and Communications Technologies (CIICT 2007). IEE, 2007. http://dx.doi.org/10.1049/cp:20070810.

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JORGENSON, PHILIP, and RODRICK CHIMA. "An explicit Runge-Kutta method for unsteady rotor/stator interaction." In 26th Aerospace Sciences Meeting. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1988. http://dx.doi.org/10.2514/6.1988-49.

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Reports on the topic "Runge-Kutta Method"

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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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