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TR-BDF2

swMATH ID:	3446
Software Authors:	Hosea, M.E.; Shampine, L.F.
Description:	Analysis and implementation of TR-BDF2 This paper deals with the successful and popular one-step method, TR-BDF2, for the solution of systems of ordinary differential equations arising in circuit and device simulation [see {it R. E. Bank}, {it W. M. Coughran jun.}, {it W. Fichtner}, {it E. H. Grosse}, {it D. J. Rose} and {it R. K. Smith}, Transient simulation of silicon devices and circuits, IEEE Trans. Comput.-Aided Design 4, 436-451 (1985)]. This method can be viewed as an embedded diagonally implicit Runge-Kutta pair of orders 2 and 3. A detailed inspection yields new results on stability, continuous extension, implementation and on improved local error estimates. Numerical examples show the effectiveness of the refined method.
Homepage:	http://ecolego.facilia.se/ecolego/show/TR-BDF2
Keywords:	numerical examples; one-step method; TR-BDF2; systems; embedded diagonally implicit Runge-Kutta pair; stability; continuous extension; error estimates
Related Software:	RODAS; Matlab; MATLAB ODE suite; ode23s; ode113; Ode15s; ode45; ode23; CHORAL; FreeFem++; MEBDF; VODE; ParaDiag; PARALAAOMPI; MGRIT; pyParareal; iFEM; TAPENADE; BEESCOUT; BEEHAVE
Cited in:	38 Publications

1 Publication describing the Software, including 1 Publication in zbMATH	Year
Analysis and implementation of TR-BDF2. Zbl 0859.65076 Hosea, M. E.; Shampine, L. F.	1996

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6	Bonaventura, Luca
3	Dumont, Yves
3	Garres-Díaz, José
3	ter Maten, E. Jan W.
2	Dufourd, Claire
2	Ehlers, Wolfgang
2	Fernández-Nieto, Enrique Domingo
2	Heider, Yousef
2	Markert, Bernd
2	Narbona-Reina, Gladys
2	Shampine, Lawrence Fred
2	Skvortsov, L. M.
1	Alexander, Roger K.
1	Allaart-Bruin, Sandra
1	Anguelov, Roumen
1	Aristizabal, F.
1	Baldazzi, Valentina
1	Bernard, Olivier
1	Boom, Pieter D.
1	Bujurke, Nagendrappa M.
1	Byrne, George D.
1	Capera-Aragones, Pau
1	Carciopolo, L. Delpopolo
1	Carpenter, Mark H.
1	Carrasco, Juan Antonio
1	Casella, Francesco
1	De Oliveira Vilaca, Luis Miguel
1	Della Rocca, A.
1	Delpopolo Carciopolo, Ludovica
1	Feldmann, Uwe
1	Fijnvandraat, J. G.
1	Formaggia, Luca
1	Foxall, Eric
1	Gendelman, Oleg V.
1	Glavinović, M. I.
1	Gómez Mármol, Macarena
1	Gouzé, Jean-Luc
1	Günther, Michael
1	Herrero, Henar
1	Hosea, M. E.
1	Houben, Stephan H. M. J.
1	Hoyas, Sergio
1	Ji, Bingquan
1	Kanso, Hussein
1	Kennedy, Christopher A.
1	Kierzenka, Jacek A.
1	Korous, Lukas
1	Liao, HongLin
1	Malhotra, Manish
1	Memah, Mohamed-Mahmoud
1	Milinkovitch, Michel C.
1	Mucientes, A. E.
1	Owhadi, Houman
1	Perchikov, Nathan
1	Peters, J. M. F.
1	Quilot-Turion, Bénédicte
1	Ranade, Abhiram G.
1	Ruiz-Baier, Ricardo
1	Salimath, Chandrasekhar
1	Scotti, Anna
1	Shiralashetti, Siddu Channabasappa
1	Šolín, Pavel
1	Suñé, Víctor
1	Thompson, Sylvester
1	Tumolo, Giovanni
1	Tyson, Rebecca C.
1	Verduyn Lunel, Sjoerd M.
1	Wang, Lin
1	Wen, Zhiwu
1	Wu, Shulin
1	Xiao, Aiguo
1	Yatat Djeumen, Ivric Valaire
1	Zhang, Lei
1	Zhang, Zhimin
1	Zhou, Tao
1	Zhu, Ting
1	Zingg, David W.
1	Zupan, Dejan
1	Zupan, Eva

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1	Computational Mechanics
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27	Numerical analysis (65-XX)
8	Ordinary differential equations (34-XX)
8	Fluid mechanics (76-XX)
8	Biology and other natural sciences (92-XX)
6	Partial differential equations (35-XX)
6	Mechanics of deformable solids (74-XX)
4	Geophysics (86-XX)
2	Probability theory and stochastic processes (60-XX)
2	Optics, electromagnetic theory (78-XX)
2	Information and communication theory, circuits (94-XX)
1	Dynamical systems and ergodic theory (37-XX)
1	Harmonic analysis on Euclidean spaces (42-XX)
1	Integral equations (45-XX)
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1	Mechanics of particles and systems (70-XX)