Relevant bibliographies by topics / Runge-Kutta method of order four

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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 of order four'

Author: Grafiati
Published: 2 June 2025
Last updated: 19 July 2025

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Journal articles on the topic "Runge-Kutta method of order four"

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Hussain, Kasim A., and Waleed J. Hasan. "Improved Runge-Kutta Method for Oscillatory Problem Solution Using Trigonometric Fitting Approach." Ibn AL-Haitham Journal For Pure and Applied Sciences 36, no. 1 (2023): 345–54. http://dx.doi.org/10.30526/36.1.2963.

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This paper provides a four-stage Trigonometrically Fitted Improved Runge-Kutta (TFIRK4) method of four orders to solve oscillatory problems, which contains an oscillatory character in the solutions. Compared to the traditional Runge-Kutta method, the Improved Runge-Kutta (IRK) method is a natural two-step method requiring fewer steps. The suggested method extends the fourth-order Improved Runge-Kutta (IRK4) method with trigonometric calculations. This approach is intended to integrate problems with particular initial value problems (IVPs) using the set functions and for trigonometrically fitte
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Olatunji, Oladayo, and Adeyemi Akeju. "Comparative Analysis of Euler and Order Four Runge-Kutta Methods in Adams-Bashforth-Moulton Predictor-Corrector Method." International Journal of Mathematics, Statistics, and Computer Science 3 (January 2, 2025): 276–93. https://doi.org/10.59543/ijmscs.v3i.10471.

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This study conducts a comparative analysis of the Euler and Runge-Kutta 4 methods within the Adams Predictor-Corrector frameworkfor solving second-order ordinary differential equations (ODEs) andcoupled differential equations. The Euler method, a basic first-orderexplicit scheme, and the Runge-Kutta 4 method, a higher-order ex-plicit scheme, are widely utilized numerical methods for ODEs. How-ever, their effectiveness varies based on the problem’s characteristics.We specifically investigate these methods integrated into the AdamsPredictor-Corrector method, renowned for its stability and effici
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Ahmad, N. A., N. Senu, and F. Ismail. "Phase-Fitted and Amplification-Fitted Higher Order Two-Derivative Runge-Kutta Method for the Numerical Solution of Orbital and Related Periodical IVPs." Mathematical Problems in Engineering 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/1871278.

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A phase-fitted and amplification-fitted two-derivative Runge-Kutta (PFAFTDRK) method of high algebraic order for the numerical solution of first-order Initial Value Problems (IVPs) which possesses oscillatory solutions is derived. We present a sixth-order four-stage two-derivative Runge-Kutta (TDRK) method designed using the phase-fitted and amplification-fitted property. The stability of the new method is analyzed. The numerical experiments are carried out to show the efficiency of the derived methods in comparison with other existing Runge-Kutta (RK) methods.
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Ahmad, S. Z., F. Ismail, N. Senu, and M. Suleiman. "Semi Implicit Hybrid Methods with Higher Order Dispersion for Solving Oscillatory Problems." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/136961.

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We constructed three two-step semi-implicit hybrid methods (SIHMs) for solving oscillatory second order ordinary differential equations (ODEs). The first two methods are three-stage fourth-order and three-stage fifth-order with dispersion order six and zero dissipation. The third is a four-stage fifth-order method with dispersion order eight and dissipation order five. Numerical results show that SIHMs are more accurate as compared to the existing hybrid methods, Runge-Kutta Nyström (RKN) and Runge-Kutta (RK) methods of the same order and Diagonally Implicit Runge-Kutta Nyström (DIRKN) method
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Hussain, Kasim Abbas. "A new embedded improved runge-kutta approach to solve first order ordinary differential equation." Journal of Interdisciplinary Mathematics 28, no. 3-B (2025): 1247–54. https://doi.org/10.47974/jim-2214.

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This work presents a novel pair of embedded improved Runge-Kutta techniques for first-order ordinary differential equations (ODEs) numerical integration. Three and four are algebraic orders for this embedded scheme. The two-step approach shown here requires fewer steps per step than the current Runge-Kutta method. The newly embedded approach efficacy in contrast to the existing embedded Runge-Kutta technique is demonstrated numerically.
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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 c
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Fikri Haiqal Faturahman, F. Armawanto, D. A. Faradita, et al. "Optimalization of Neural Network Method on Harmonis Damped Swing." Jurnal Pendidikan Fisika Undiksha 13, no. 3 (2023): 370–81. https://doi.org/10.23887/jjpf.v13i3.70347.

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Numerical methods are used to solve the differential equations in the case of a damped pendulum system. In this paper, we aim to solve the equation of dumped pendulum motion using some numerical. Four numerical methods are decomposed, each the Euler method, fourth-order Runge-Kutte, Odeint provided in Python, and Neural Network scheme. All answers obtained are approximations or predictions that include errors. The error of those methods will be compared with the analytical solution of the case, known as the global error. The Odeint and fourth-order Runge-Kutta methods are more accurate than th
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Lawal, Jibril* Ibrahim MaiHaja &. Ibrahim M. O. "SOLUTION OF CHOLERA CARRIER EPIDEMIC MODEL USING DIFFERENTIAL TRANSFORM METHOD (DTM)." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 7, no. 1 (2018): 242–49. https://doi.org/10.5281/zenodo.1136136.

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In this paper, Differential Transform Method (DTM) is applied to the deterministic mathematical model of cholera carrier epidemic. The model is transformed using DTM operational properties, hence, the power series of the model system is generated and also an approximate solution of the model was established. The accuracy of DTM is demonstrated against Fehlberg Runge-Kutta method with order four interpolant (RKF-45) numerical solution and it demonstrated high accuracy of the results. Plotted DTM solution is found to be in good agreement with the popular Runge-Kutta solution.In this paper, Diffe
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Ghazal, Zainab Khaled, and Kasim Abbas Hussain. "Solving Oscillating Problems Using Modifying Runge-Kutta Methods." Ibn AL- Haitham Journal For Pure and Applied Sciences 34, no. 4 (2021): 58–67. http://dx.doi.org/10.30526/34.4.2703.

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This paper develop conventional Runge-Kutta methods of order four and order five to solve ordinary differential equations with oscillating solutions. The new modified Runge-Kutta methods (MRK) contain the invalidation of phase lag, phase lag’s derivatives, and amplification error. Numerical tests from their outcomes show the robustness and competence of the new methods compared to the well-known Runge-Kutta methods in the scientific literature.
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Rabiei, Faranak, Fudziah Ismail, Ali Ahmadian, and Soheil Salahshour. "Numerical Solution of Second-Order Fuzzy Differential Equation Using Improved Runge-Kutta Nystrom Method." Mathematical Problems in Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/803462.

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We develop the Fuzzy Improved Runge-Kutta Nystrom (FIRKN) method for solving second-order fuzzy differential equations (FDEs) based on the generalized concept of higher-order fuzzy differentiability. The scheme is two-step in nature and requires less number of stages which leads to less number of function evaluations in comparison with the existing Fuzzy Runge-Kutta Nystrom method. Therefore, the new method has a lower computational cost which effects the time consumption. We assume that the fuzzy function and its derivative are Hukuhara differentiable. FIRKN methods of orders three, four, and
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Dissertations / Theses on the topic "Runge-Kutta method of order four"

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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
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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 inte
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Alhojilan, Yazid Yousef M. "Higher-order numerical scheme for solving stochastic differential equations." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/15973.

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We present a new pathwise approximation method for stochastic differential equations driven by Brownian motion which does not require simulation of the stochastic integrals. The method is developed to give Wasserstein bounds O(h3/2) and O(h2) which are better than the Euler and Milstein strong error rates O(√h) and O(h) respectively, where h is the step-size. It assumes nondegeneracy of the diffusion matrix. We have used the Taylor expansion but generate an approximation to the expansion as a whole rather than generating individual terms. We replace the iterated stochastic integrals in the met
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Jewell, Jeffrey Steven. "Higher-order Runge--Kutta type schemes based on the Method of Characteristics for hyperbolic equations with crossing characteristics." ScholarWorks @ UVM, 2019. https://scholarworks.uvm.edu/graddis/1028.

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The Method of Characteristics (MoC) is a well-known procedure used to find the numerical solution of systems of hyperbolic partial differential equations (PDEs). The main idea of the MoC is to integrate a system of ordinary differential equations (ODEs) along the characteristic curves admitted by the PDEs. In principle, this can be done by any appropriate numerical method for ODEs. In this thesis, we will examine the MoC applied to systems of hyperbolic PDEs with straight-line and crossing characteristics. So far, only first- and second-order accurate explicit MoC schemes for these types of sy
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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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Villardi, de Montlaur Adeline de. "High-order discontinuous Galerkin methods for incompressible flows." Doctoral thesis, Universitat Politècnica de Catalunya, 2009. http://hdl.handle.net/10803/5928.

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Aquesta tesi doctoral proposa formulacions de Galerkin discontinu (DG) d'alt ordre per fluxos viscosos incompressibles. <br/>Es desenvolupa un nou mètode de DG amb penalti interior (IPM-DG), que condueix a una forma feble simètrica i coerciva pel terme de difusió, i que permet assolir una aproximació espacial d'alt ordre. Aquest mètode s'aplica per resoldre les equacions de Stokes i Navier-Stokes. L'espai d'aproximació de la velocitat es descompon dins de cada element en una part solenoidal i una altra irrotacional, de manera que es pot dividir la forma dèbil IPM-DG en dos problemes desacoblat
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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 system
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N'guessan, Marc-Arthur. "Space adaptive methods with error control based on adaptive multiresolution for the simulation of low-Mach reactive flows." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASC017.

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Ce travail vise au développement de nouvelles méthodes numériques adaptatives pour la simulation numérique de phénomènes physiques multi-échelles en temps et en espace. Nous nous concentrons sur les écoulements réactifs à faible nombre de Mach, caractéristiques d'un grand nombre de configurations industrielles telles que la convection naturelle, la dynamique de fronts de flamme ou encore les décharges plasmas. La raideur associée à ce type de problèmes, que ce soit via le terme source chimique qui présente un large spectre d'échelles de temps caractéristiques ou encore via la présence de forts
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Meng-HanLi and 李孟翰. "A High-Order Runge-Kutta Discontinuous Galerkin Method for The Two-Dimensional Wave Equation." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/60562488311569777411.

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碩士<br>國立成功大學<br>數學系應用數學碩博士班<br>98<br>In this work, we develop a high-order Runge-Kutta Discontinuous Galerkin (RKDG) method to solve the two-dimensional wave equations. We use DG methods to discretize the equations with high order elements in space, and then we use the mth-order, m-stage strong stability preserving Runge-Kutta (SSP-RK) scheme to solve the resulting semi-discrete equations. To discretize the equaiotns in spaces, we use the quadrilateral elements and the Q^k-polynomials as basis functions. The scheme achieves full high-order convergence in time and space while keeping the time-s
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Kotovshchikova, Marina. "On a third-order FVTD scheme for three-dimensional Maxwell's Equations." 2016. http://hdl.handle.net/1993/31035.

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This thesis considers the application of the type II third order WENO finite volume reconstruction for unstructured tetrahedral meshes proposed by Zhang and Shu in (CCP, 2009) and the third order multirate Runge-Kutta time-stepping to the solution of Maxwell's equations. The dependance of accuracy of the third order WENO scheme on the small parameter in the definition of non-linear weights is studied in detail for one-dimensional uniform meshes and numerical results confirming the theoretical analysis are presented for the linear advection equation. This analysis is found to be crucial in the
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Books on the topic "Runge-Kutta method of order four"

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National Institute of Standards and Technology (U.S.), ed. Parallelizing a fourth-order Runge-Kutta method. U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 1997.

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National Institute of Standards and Technology (U.S.), ed. Parallelizing a fourth-order Runge-Kutta method. U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 1997.

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National Institute of Standards and Technology (U.S.), ed. Parallelizing a fourth-order Runge-Kutta method. U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 1997.

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National Institute of Standards and Technology (U.S.), ed. Parallelizing a fourth-order Runge-Kutta method. U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 1997.

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National Institute of Standards and Technology (U.S.), ed. Parallelizing a fourth-order Runge-Kutta method. U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 1997.

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National Institute of Standards and Technology (U.S.), ed. Parallelizing a fourth-order Runge-Kutta method. U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 1997.

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National Institute of Standards and Technology (U.S.), ed. Parallelizing a fourth-order Runge-Kutta method. U.S. Dept. of Commerce, Technology Administration, National Institute of Standards and Technology, 1997.

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

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O, Demuren Ayodeji, Carpenter Mark, and Institute for Computer Applications in Science and Engineering., eds. Higher-order compact schemes for numerical simulation of incompressible flows. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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O, Demuren A., Carpenter Mark, and Institute for Computer Applications in Science and Engineering., eds. Higher-order compact schemes for numerical simulation of incompressible flows. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1998.

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Book chapters on the topic "Runge-Kutta method of order four"

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

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Sundnes, Joakim. "Stable Solvers for Stiff ODE Systems." In Solving Ordinary Differential Equations in Python. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-46768-4_3.

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AbstractIn the previous chapter, we introduced explicit Runge-Kutta (ERK) methods and demonstrated how they can be implemented as a hierarchy of Python classes. For most ODE systems, replacing the simple forward Euler method with a higher-order ERK method will significantly reduce the number of time steps needed to reach a specified accuracy. Furthermore, it often leads to reduced computation time, since the additional cost per time step is outweighed by the reduced number of steps. However, there exists a class of ODEs known as stiff systems, where all the ERK methods require very small time steps, and any attempt to increase the time step leads to spurious oscillations and possible divergence of the solution. Stiff ODE systems pose a challenge for explicit methods, and they are better addressed by implicit solvers such as implicit Runge-Kutta (IRK) methods. IRK methods are well-suited for stiff problems and can offer substantial reductions in computation time when tackling challenging problems.
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Demba, Musa A., Norazak Senu, and Fudziah Ismail. "Fifth-Order Four-Stage Explicit Trigonometrically-Fitted Runge–Kutta–Nyström Methods." In Recent Advances in Mathematical Sciences. Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-0519-0_3.

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Zhang, Baoji, and Lupeng Fu. "Study on the Analysis Method of Ship Surf-Riding/Broaching Based on Maneuvering Equations." In Proceeding of 2021 International Conference on Wireless Communications, Networking and Applications. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-2456-9_58.

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AbstractIn order to understand the mechanism of the surf-riding/broaching profoundly, the four- degree- of-freedom(4DOF) maneuvering equation (surge, sway, yaw and roll) is simplified to a one- degree-of-freedom (1DOF) equation, and the fourth-order Runge-Kutta method is used to integrate a 1DOF surge equation in the time domain to analyze the two motion states of the ship during the surging and surf-riding. The critical Froude number is calculated using the Melnikov method. Taking a fishing boat as an example, the ship’s surf-riding/broaching phenomenon is simulated under the condition of wavelength-to-ship-length ratio and wave steepness, 1 and 1/10 respectively, providing technical support for the formulation of the second generation intact stability criteria.
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Rabiei, Faranak, Fudziah Ismail, Norihan Arifin, and Saeid Emadi. "Third Order Accelerated Runge-Kutta Nyström Method for Solving Second-Order Ordinary Differential Equations." In Informatics Engineering and Information Science. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-25462-8_17.

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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. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-24289-3_8.

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Ben Amma, B., Said Melliani, and L. S. Chadli. "A Fourth Order Runge-Kutta Gill Method for the Numerical Solution of Intuitionistic Fuzzy Differential Equations." In Recent Advances in Intuitionistic Fuzzy Logic Systems. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02155-9_5.

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Luan, Vu Thai, and Alexander Ostermann. "Stiff Order Conditions for Exponential Runge–Kutta Methods of Order Five." In Modeling, Simulation and Optimization of Complex Processes - HPSC 2012. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09063-4_11.

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Hairer, Ernst, Michel Roche, and Christian Lubich. "Order conditions of Runge-Kutta methods for index 2 systems." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0093952.

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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. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-25255-6_25.

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Conference papers on the topic "Runge-Kutta method of order four"

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Thomas, Reetha, S. Maheswari, and S. Narayanamoorthy. "Glucose-insulin regulatory model using Runge Kutta method of order four." In PROCEEDINGS OF INTERNATIONAL CONFERENCE ON ADVANCES IN MATERIALS RESEARCH (ICAMR - 2019). AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0017202.

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Lin, Ruitao, Chan Wang, Fang Liu, and Yueliang Xu. "A new numerical method of nonlinear equations by four order Runge-Kutta method." In EM). IEEE, 2010. http://dx.doi.org/10.1109/ieem.2010.5674394.

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Hussain, Kasim, Fudziah Ismail, Norazak Senu, and Faranak Rabiei. "Optimized fourth-order Runge-Kutta method for solving oscillatory problems." In INNOVATIONS THROUGH MATHEMATICAL AND STATISTICAL RESEARCH: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics (ICMSS2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4952512.

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Fabien, Brian C. "Dynamic System Optimization Using Higher-Order Runge-Kutta Discretization." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-39421.

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This paper evaluates some numerical methods for the approximate solution dynamic system optimization problems. The paper considers the optimization of dynamic systems that are subject to equality and inequality constraints. These types of problems include optimal control and parameter identification optimization problems. The numerical solution technique is based on transforming the infinite dimensional dynamic system optimization problem into a finite dimensional nonlinear programming (NLP) problem. This solution method is realized by; (i) approximating the control input using a finite set of
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Zhang, Zhizhu, and Yun Cai. "A Numerical Solution to the Point Kinetic Equations Using Diagonally Implicit Runge Kutta Method." In 2016 24th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/icone24-60011.

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It would take a long time to solve the point kinetics equations by using full implicit Runge-Kutta (FIRK) for the strong stiffness. Diagonally implicit Runge-Kutta (DIRK) is a useful tool like FIRK to solve the stiff differential equations, while it could greatly reduce the computation compared to FIRK. By embedded low-order Runge-Kutta, DIRK is implemented with the time step adaptation technique, which improves the computation efficiency of DIRK. Through four typical cases with step, ramp sinusoidal and zig-zag reactivity insertions, it shows that the results obtained by DIRK are in perfect a
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Wing, Moo Kwong, Norazak Senu, Fudziah Ismail, and Mohamed Suleiman. "A fourth order phase-fitted Runge-Kutta-Nyström method for oscillatory problems." In PROCEEDINGS OF THE 20TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES: Research in Mathematical Sciences: A Catalyst for Creativity and Innovation. AIP, 2013. http://dx.doi.org/10.1063/1.4801141.

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Fawzi, Firas Adel, N. Senu, F. Ismail, and Z. A. Majid. "Explicit Runge-Kutta method with trigonometrically-fitted for solving first order ODEs." In INNOVATIONS THROUGH MATHEMATICAL AND STATISTICAL RESEARCH: Proceedings of the 2nd International Conference on Mathematical Sciences and Statistics (ICMSS2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4952524.

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A, Ezhilarasi. "A Study of Runge-Kutta Method for n-th Order Differential Equations." In 2023 2nd International Conference on Advancements in Electrical, Electronics, Communication, Computing and Automation (ICAECA). IEEE, 2023. http://dx.doi.org/10.1109/icaeca56562.2023.10200469.

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Ismail, Fudziah, and Mohammed M. Salih. "Diagonally implicit Runge-Kutta method of order four with minimum phase-lag for solving first order linear ODEs." In PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4885049.

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Jikantoro, Yusuf Dauda, Fudziah Ismail, and Noraz Senu. "A new fourth-order explicit Runge-Kutta method for solving first order ordinary differential equations." In PROCEEDINGS OF THE 20TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES: Research in Mathematical Sciences: A Catalyst for Creativity and Innovation. AIP, 2013. http://dx.doi.org/10.1063/1.4801239.

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Reports on the topic "Runge-Kutta method of order four"

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

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Trahan, Corey, Jing-Ru Cheng, and Amanda Hines. ERDC-PT : a multidimensional particle tracking model. Engineer Research and Development Center (U.S.), 2023. http://dx.doi.org/10.21079/11681/48057.

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Abstract:
This report describes the technical engine details of the particle- and species-tracking software ERDC-PT. The development of ERDC-PT leveraged a legacy ERDC tracking model, “PT123,” developed by a civil works basic research project titled “Efficient Resolution of Complex Transport Phenomena Using Eulerian-Lagrangian Techniques” and in part by the System-Wide Water Resources Program. Given hydrodynamic velocities, ERDC-PT can track thousands of massless particles on 2D and 3D unstructured or converted structured meshes through distributed processing. At the time of this report, ERDC-PT support
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