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Relevant bibliographies by topics / Implicit Runge-Kutta method

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Academic literature on the topic 'Implicit Runge-Kutta method'

Author: Grafiati

Published: 10 March 2023

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Journal articles on the topic "Implicit Runge-Kutta method"

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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 o

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Hasan, M. Kamrul, M. Suzan Ahamed, M. S. Alam, and M. Bellal Hossain. "An Implicit Method for Numerical Solution of Singular and Stiff Initial Value Problems." Journal of Computational Engineering 2013 (September 26, 2013): 1–5. http://dx.doi.org/10.1155/2013/720812.

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An implicit method has been presented for solving singular initial value problems. The method is simple and gives more accurate solution than the implicit Euler method as well as the second order implicit Runge-Kutta (RK2) (i.e., implicit midpoint rule) method for some particular singular problems. Diagonally implicit Runge-Kutta (DIRK) method is suitable for solving stiff problems. But, the derivation as well as utilization of this method is laborious. Sometimes it gives almost similar solution to the two-stage third order diagonally implicit Runge-Kutta (DIRK3) method and the five-stage fift

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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 (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

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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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IMAI, Yohsuke, Takayuki Aoki, and Tetsuya Kobara. "Implicit IDO scheme by using Runge-Kutta method." Proceedings of The Computational Mechanics Conference 2003.16 (2003): 151–52. http://dx.doi.org/10.1299/jsmecmd.2003.16.151.

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Janezic, Dusanka, and Bojan Orel. "Implicit Runge-Kutta method for molecular dynamics integration." Journal of Chemical Information and Modeling 33, no. 2 (1993): 252–57. http://dx.doi.org/10.1021/ci00012a011.

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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 (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 met

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Gardner, David J., Jorge E. Guerra, François P. Hamon, Daniel R. Reynolds, Paul A. Ullrich, and Carol S. Woodward. "Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models." Geoscientific Model Development 11, no. 4 (2018): 1497–515. http://dx.doi.org/10.5194/gmd-11-1497-2018.

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Abstract. The efficient simulation of non-hydrostatic atmospheric dynamics requires time integration methods capable of overcoming the explicit stability constraints on time step size arising from acoustic waves. In this work, we investigate various implicit–explicit (IMEX) additive Runge–Kutta (ARK) methods for evolving acoustic waves implicitly to enable larger time step sizes in a global non-hydrostatic atmospheric model. The IMEX formulations considered include horizontally explicit – vertically implicit (HEVI) approaches as well as splittings that treat some horizontal dynamics implicitly

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Huang, Juntao, and Chi-Wang Shu. "A second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin scheme for the Kerr–Debye model." Mathematical Models and Methods in Applied Sciences 27, no. 03 (2017): 549–79. http://dx.doi.org/10.1142/s0218202517500099.

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In this paper, we develop a second-order asymptotic-preserving and positivity-preserving discontinuous Galerkin (DG) scheme for the Kerr–Debye model. By using the approach first introduced by Zhang and Shu in [Q. Zhang and C.-W. Shu, Error estimates to smooth solutions of Runge–Kutta discontinuous Galerkin methods for scalar conservation laws, SIAM J. Numer. Anal. 42 (2004) 641–666.] with an energy estimate and Taylor expansion, the asymptotic-preserving property of the semi-discrete DG methods is proved rigorously. In addition, we propose a class of unconditional positivity-preserving implici

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Cong, Y. H., and C. X. Jiang. "Diagonally Implicit Symplectic Runge-Kutta Methods with High Algebraic and Dispersion Order." Scientific World Journal 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/147801.

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The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper. A diagonally implicit symplectic nine-stages Runge-Kutta method with algebraic order 6 and dispersion order 8 is presented. Numerical experiments with some Hamiltonian oscillatory problems are presented to show the proposed method is as competitive as the existing same type Runge-Kutta methods.

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Dissertations / Theses on the topic "Implicit Runge-Kutta method"

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Roberts, Steven Byram. "Multimethods for the Efficient Solution of Multiscale Differential Equations." Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/104872.

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Mathematical models involving ordinary differential equations (ODEs) play a critical role in scientific and engineering applications. Advances in computing hardware and numerical methods have allowed these models to become larger and more sophisticated. Increasingly, problems can be described as multiphysics and multiscale as they combine several different physical processes with different characteristics. If just one part of an ODE is stiff, nonlinear, chaotic, or rapidly-evolving, this can force an expensive method or a small timestep to be used. A method which applies a discretization a

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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 d

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Biehn, Neil David. "Implicit Runge-Kutta Methods for Stiff and Constrained Optimal Control Problems." NCSU, 2001. http://www.lib.ncsu.edu/theses/available/etd-20010322-165913.

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<p>The purpose of the research presented in this thesis is to better understand and improve direct transcription methods for stiff and state constrained optimal control problems. When some implicit Runge-Kutta methods are implemented as approximations to the dynamics of an optimal control problem, a loss of accuracy occurs when the dynamics are stiff or constrained. A new grid refinement strategy which exploits the variation of accuracy is discussed. In addition, the use of a residual function in place of classical error estimation techniques is proven to work well for stiff systems. Computati

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Al-Harbi, Saleh M. "Implicit Runge-Kutta methods for the numerical solution of stiff ordinary differential equation." Thesis, University of Manchester, 1999. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.488322.

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The primary aim of this thesis is to calculate the numerical solution of a given stiff system of ordinary differential equations. We deal with the implementation of the implicit Runge-Kutta methods, in particular for Radau IIA order 5 which is now a competitive method for solving stiff initial value problems. New software based on Radau IIA, called IRKMR5 written in MATLAB has been developed for fixed order (order 5) with variable stepsizes, which is quite efficient when it is used to solve stiff problems. The code is organized in a modular form so that it facilitates both the understanding of

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Wood, Dylan M. "Solving Unsteady Convection-Diffusion Problems in One and More Dimensions with Local Discontinuous Galerkin Methods and Implicit-Explicit Runge-Kutta Time Stepping." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1461181441.

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Santos, Ricardo Dias dos. "Uma formulação implícita para o método Smoothed Particle Hydrodynamics." Universidade do Estado do Rio de Janeiro, 2014. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=6751.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>Em uma grande gama de problemas físicos, governados por equações diferenciais, muitas vezes é de interesse obter-se soluções para o regime transiente e, portanto, deve-se empregar técnicas de integração temporal. Uma primeira possibilidade seria a de aplicar-se métodos explícitos, devido à sua simplicidade e eficiência computacional. Entretanto, esses métodos frequentemente são somente condicionalmente estáveis e estão sujeitos a severas restrições na escolha do passo no tempo. Para problemas advectivos, governados por equações hip

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Scandurra, Leonardo. "Numerical Methods for All Mach Number flows for Gas Dynamics." Doctoral thesis, Università di Catania, 2017. http://hdl.handle.net/10761/4042.

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An original numerical method to solve the all-Mach number flow for the Euler equations of gas dynamics on staggered grid is presented in this thesis. The system is discretized to second order in space on staggered grid, in a fashion similar to the Nessyahu-Tadmor central scheme for 1D model and Jang-Tadmor central scheme for 2D model, thus simplifying the flux computation. This approach turns out to be extremely simple, since it requires no equation splitting. We consider the isentropic case and the general case. For simplicity we assume a gamma-law gas in both cases. Both approaches are bas

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AbuAlSaud, Moataz. "Simulation of 2-D Compressible Flows on a Moving Curvilinear Mesh with an Implicit-Explicit Runge-Kutta Method." Thesis, 2012. http://hdl.handle.net/10754/244571.

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The purpose of this thesis is to solve unsteady two-dimensional compressible Navier-Stokes equations for a moving mesh using implicit explicit (IMEX) Runge- Kutta scheme. The moving mesh is implemented in the equations using Arbitrary Lagrangian Eulerian (ALE) formulation. The inviscid part of the equation is explicitly solved using second-order Godunov method, whereas the viscous part is calculated implicitly. We simulate subsonic compressible flow over static NACA-0012 airfoil at different angle of attacks. Finally, the moving mesh is examined via oscillating the airfoil between angle of at

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Roskovec, Filip. "Numerické řešení nelineárních problémů konvekce-difuze pomocí adaptivních metod." Master's thesis, 2014. http://www.nusl.cz/ntk/nusl-340765.

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This thesis is concerned with analysis and implementation of Time discontinuous Galerkin method. Important part of it is constructing of algorithm for solving nonlinear convection-diffusion equations, which combines Discontinuous Galerkin method in space (DGFEM) with Time discontinuous Galerkin method (TDG). Nonlinearity of the problem is overcome by damped Newton-like method. This approach provides easy adaptivity manipulation as well as high order approximation with respect to both space and time variables. The second part of the thesis is focused on Time discontinuous Galerkin method, appli

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FRASCA, CACCIA GIANLUCA. "A new efficient implementation for HBVMs and their application to the semilinear wave equation." Doctoral thesis, 2015. http://hdl.handle.net/2158/992629.

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In this thesis we have provided a detailed description of the low-rank Runge-Kutta family of Hamiltonian Boundary Value Methods (HBVMs) for the numerical solution of Hamiltonian problems. In particular, we have studied in detail their main property: the conservation of polynomial Hamiltonians, which results into a practical conservation for generic suitably regular Hamiltonians. This property turns out to play a fundamental role in some problems where the error on the Hamiltonian, usually obtained even when using a symplectic method, would be not negligible to the point of affecting the dynami

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Books on the topic "Implicit Runge-Kutta method"

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

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Center, Langley Research, ed. On implicit Runge-Kutta methods for parallel computations. National Aeronautics and Space Administration, Langley Research Center, 1987.

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Center, Langley Research, ed. On implicit Runge-Kutta methods for parallel computations. National Aeronautics and Space Administration, Langley Research Center, 1987.

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Loon, M. van. Time-step enlargement for Runge-Kutta integration algorithms by implicit smoothing. National Aerospace Laboratory, 1991.

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Davidson, Lars. Implementation of a semi-implicit k-e turbulence model into an explicit Runge-Kutta Navier-Stokes code. CERFACS, 1990.

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United States. National Aeronautics and Space Administration., ed. Flow simulations about steady-complex and unsteady moving configurations using structured-overlapped and unstructured grids: Abstract. National Aeronautics and Space Administration, 1995.

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Nguyen, Hung. Interpolation and error control schemes for algebraic differential equations using continuous implicit Runge-Kutta methods. University of Toronto, Dept. of Computer Science, 1995.

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Book chapters on the topic "Implicit Runge-Kutta method"

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Hecke, T., M. Daele, G. Berghe, and H. Meyer. "P-stable mono-implicit Runge-Kutta-Nyström modifications of the Numerov method." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3-540-62598-4_135.

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Bouhamidi, A., and K. Jbilou. "A Fast Block Krylov Implicit Runge–Kutta Method for Solving Large-Scale Ordinary Differential Equations." In Optimization, Simulation, and Control. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-5131-0_20.

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

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

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Hairer, Ernst, and Gerhard Wanner. "Implementation of Implicit Runge-Kutta Methods." In Springer Series in Computational Mathematics. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-05221-7_8.

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Strehmel, Karl, and Rüdiger Weiner. "Linear-implizite Runge-Kutta-Methoden." In Teubner-Texte zur Mathematik. Vieweg+Teubner Verlag, 1992. http://dx.doi.org/10.1007/978-3-663-10673-9_4.

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Strehmel, Karl, and Rüdiger Weiner. "Partitionierte linear-implizite Runge-Kutta-Methoden." In Teubner-Texte zur Mathematik. Vieweg+Teubner Verlag, 1992. http://dx.doi.org/10.1007/978-3-663-10673-9_5.

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Trobec, Roman, Bojan Orel, and Boštjan Slivnik. "Coarse-grain parallelisation of multi-implicit Runge-Kutta methods." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/3-540-62598-4_131.

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Lindblad, E., D. M. Valiev, B. Müller, J. Rantakokko, P. Lütstedt, and M. A. Liberman. "Implicit-explicit Runge-Kutta methods for stiff combustion problems." In Shock Waves. Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-85168-4_47.

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Cordero-Carrión, Isabel, and Pablo Cerdá-Durán. "Partially Implicit Runge-Kutta Methods for Wave-Like Equations." In Advances in Differential Equations and Applications. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06953-1_26.

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Conference papers on the topic "Implicit Runge-Kutta method"

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Ma, Can, Xinrong Su, Jinlan Gou, and Xin Yuan. "Runge-Kutta/Implicit Scheme for the Solution of Time Spectral Method." In ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/gt2014-26474.

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This paper investigates the Runge-Kutta implicit scheme applied to the solution of the time spectral method for periodic unsteady flow simulation. Several explicit and implicit time integration schemes including the Runge-Kutta scheme, Block-Jacobi SSOR (symmetric successive over relaxation)scheme and Block-Jacobi Runge-Kutta/Implicit scheme are implemented into an in-house code and applied to the time marching solution of the time spectral method. The time integration is coupled with Full Approximation Storage (FAS) type multi-grid method for convergence acceleration. The in-house code is bas

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Kalogiratou, Zacharoula, Theodore Monovasilis, and T. E. Simos. "A sixth order symmetric and symplectic diagonally implicit Runge-Kutta method." In INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING 2014 (ICCMSE 2014). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4897862.

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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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Kalogiratou, Z., Th Monovasilis, T. E. Simos, et al. "A Diagonally Implicit Symplectic Runge-Kutta Method with Minimum Phase-lag." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3637001.

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Do, Nguyen B., Aldo A. Ferri, and Olivier Bauchau. "Efficient Simulation of a Dynamic System With LuGre Friction." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85339.

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Friction is a difficult phenomenon to model and simulate. One promising friction model is the LuGre model, which captures key frictional behavior from experiments and from other friction laws. While displaying many modeling advantages, the LuGre model of friction can result in numerically stiff system dynamics. In particular, the LuGre friction model exhibits very slow dynamics during periods of sticking and very fast dynamics during periods of slip. This paper investigates the best simulation strategies for application to dynamic systems with LuGre friction. Several simulation strategies are

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SENU, N., M. SULEIMAN, F. ISMAIL, and M. OTHMAN. "A SINGLY DIAGONALLY IMPLICIT RUNGE-KUTTA-NYSTRÖM METHOD WITH DISPERSION OF HIGH ORDER." In Special Edition of the International MultiConference of Engineers and Computer Scientists 2011. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814390019_0009.

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Liu, P. F., H. Wei, B. Li, and B. Zhou. "Transient stability constrained optimal power flow using 2-stage diagonally implicit Runge-Kutta method." In 2013 IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC). IEEE, 2013. http://dx.doi.org/10.1109/appeec.2013.6837193.

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Wing, Moo Kwong, Norazak Senu, Mohamed Suleiman, and Fudziah Ismail. "A five-stage singly diagonally implicit Runge-Kutta-Nyström method with reduced phase-lag." In INTERNATIONAL CONFERENCE ON FUNDAMENTAL AND APPLIED SCIENCES 2012: (ICFAS2012). AIP, 2012. http://dx.doi.org/10.1063/1.4757486.

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Franco, Michael, Per-Olof Persson, Will Pazner, and Matthew J. Zahr. "An Adjoint Method using Fully Implicit Runge-Kutta Schemes for Optimization of Flow Problems." In AIAA Scitech 2019 Forum. American Institute of Aeronautics and Astronautics, 2019. http://dx.doi.org/10.2514/6.2019-0351.

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Zhang, Yining, Haochun Zhang, Yang Su, and Guangbo Zhao. "A Comparative Study of 10 Different Methods on Numerical Solving of Point Reactor Neutron Kinetics Equations." In 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-67275.

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Point reactor neutron kinetics equations describe the time dependent neutron density variation in a nuclear reactor core. These equations are widely applied to nuclear system numerical simulation and nuclear power plant operational control. This paper analyses the characteristics of 10 different basic or normal methods to solve the point reactor neutron kinetics equations. These methods are: explicit and implicit Euler method, explicit and implicit four order Runge-Kutta method, Taylor polynomial method, power series method, decoupling method, end point floating method, Hermite method, Gear me

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