L. M. Skvortsov, “Diagonally implicit Runge-Kutta methods for differential-algebraic equations of indices 2 and 3”, Zh. Vychisl. Mat. Mat. Fiz., 50:6 (2010), 1047–1059; Comput. Math. Math. Phys., 50:6 (2010), 993

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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2010, Volume 50, Number 6, Pages 1047–1059 (Mi zvmmf4890)

This article is cited in 15 scientific papers (total in 15 papers)

Diagonally implicit Runge-Kutta methods for differential-algebraic equations of indices 2 and 3

L. M. Skvortsov

Bauman State Technical University, Vtoraya Baumanskaya ul. 5, Moscow, 105005 Russia

Full-text PDF (328 kB) Citations (15)

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Abstract: Diagonally implicit Runge-Kutta methods satisfying additional order conditions are examined. These conditions make it possible to solve differential algebraic equations of indices two and three to higher accuracy. Advantages of the proposed methods over other known techniques are demonstrated using test problems.

Key words: differential algebraic equations, differentiation index, diagonally implicit Runge–Kutta methods, SDIRK method, ESDIRK method.

Received: 07.10.2009

English version:
Computational Mathematics and Mathematical Physics, 2010, Volume 50, Issue 6, Pages 993–1005
DOI: https://doi.org/10.1134/S0965542510060072

Bibliographic databases:

Document Type: Article

UDC: 519.62

Language: Russian

Citation: L. M. Skvortsov, “Diagonally implicit Runge-Kutta methods for differential-algebraic equations of indices 2 and 3”, Zh. Vychisl. Mat. Mat. Fiz., 50:6 (2010), 1047–1059; Comput. Math. Math. Phys., 50:6 (2010), 993–1005

Citation in format AMSBIB

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Linking options:

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This publication is cited in the following 15 articles:

Yunzhu Cai, Jiawei Wan, Ahsan Kareem, “On convergence of implicit Runge-Kutta methods for the incompressible Navier-Stokes equations with unsteady inflow”, Journal of Computational Physics, 523 (2025), 113627
L. M. Skvortsov, “Generalizations of the Stage Order of Runge–Kutta Methods”, Comput. Math. and Math. Phys., 64:12 (2024), 2796
Juan Tang, Jianguang Lu, “Modified Extended Lie-Group Method for Hessenberg Differential Algebraic Equations with Index-3”, Mathematics, 11:10 (2023), 2360
L. M. Skvortsov, “Third- and fourth-order ESDIRK methods for stiff and differential-algebraic problems”, Comput. Math. Math. Phys., 46:5 (2022), 766–783
Yin L., Yang Ch., Ma Sh.-Zh., Zhang K.-K., “Parallel and Fully Implicit Simulations of the Thermal Convection in the Earth'S Outer Core”, Comput. Fluids, 193 (2019), UNSP 104278
Boom P.D., Zingg D.W., “Optimization of High-Order Diagonally-Implicit Runge-Kutta Methods”, J. Comput. Phys., 371 (2018), 168–191
L. M. Skvortsov, “How to avoid accuracy and order reduction in Runge–Kutta methods as applied to stiff problems”, Comput. Math. Math. Phys., 57:7 (2017), 1124–1139
Blom D.S., Birken Ph., Bijl H., Kessels F., Meister A., van Zuijlen A.H., “A comparison of Rosenbrock and ESDIRK methods combined with iterative solvers for unsteady compressible flows”, Adv. Comput. Math., 42:6 (2016), 1401–1426
Joachim Rang, “High order time discretisation methods for incompressible Navier–Stokes equations”, Proc Appl Math and Mech, 16:1 (2016), 759
Rang J., “An Analysis of the Prothero-Robinson Example For Constructing New Adaptive Esdirk Methods of Order 3 and 4”, Appl. Numer. Math., 94 (2015), 75–87
L. M. Skvortsov, O. S. Kozlov, “Efficient implementation of diagonally implicit Runge–Kutta methods”, Math. Models Comput. Simul., 6:4 (2014), 415–424
L. M. Skvortsov, “Singly implicit diagonally extended Runge–Kutta methods of fourth order”, Comput. Math. Math. Phys., 54:5 (2014), 775–784
Rang J., “An Analysis of the Prothero-Robinson Example For Constructing New Dirk and Row Methods”, J. Comput. Appl. Math., 262 (2014), 105–114
Yan Zeng, Xuesong Wu, Jianwen Cao, “Research and Implementation of Hungarian Method Based on the Structure Index Reduction for DAE Systems”, Journal of Algorithms & Computational Technology, 8:2 (2014), 219
L. M. Skvortsov, “Runge–Kutta collocation methods for differential-algebraic equations of indices 2 and 3”, Comput. Math. Math. Phys., 52:10 (2012), 1373–1383

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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