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.

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  1. Bonaventura, Luca; Casella, F.; Carciopolo, L. Delpopolo; Ranade, A.: A self adjusting multirate algorithm for robust time discretization of partial differential equations (2020)
  2. Kanso, Hussein; Quilot-Turion, Bénédicte; Memah, Mohamed-Mahmoud; Bernard, Olivier; Gouzé, Jean-Luc; Baldazzi, Valentina: Reducing a model of sugar metabolism in peach to catch different patterns among genotypes (2020)
  3. Delpopolo Carciopolo, Ludovica; Bonaventura, Luca; Scotti, Anna; Formaggia, Luca: A conservative implicit multirate method for hyperbolic problems (2019)
  4. De Oliveira Vilaca, Luis Miguel; Milinkovitch, Michel C.; Ruiz-Baier, Ricardo: Numerical approximation of a 3D mechanochemical interface model for skin patterning (2019)
  5. Bonaventura, Luca; Fernández-Nieto, Enrique D.; Garres-Díaz, José; Narbona-Reina, Gladys: Multilayer shallow water models with locally variable number of layers and semi-implicit time discretization (2018)
  6. Boom, Pieter D.; Zingg, David W.: Optimization of high-order diagonally-implicit Runge-Kutta methods (2018)
  7. Perchikov, Nathan; Gendelman, O. V.: Transient dynamics in strongly nonlinear systems: optimization of initial conditions on the resonant manifold (2018)
  8. Anguelov, Roumen; Dufourd, Claire; Dumont, Yves: Mathematical model for pest-insect control using mating disruption and trapping (2017)
  9. Bonaventura, L.; Della Rocca, A.: Unconditionally strong stability preserving extensions of the TR-BDF2 method (2017)
  10. Owhadi, Houman; Zhang, Lei: Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients (2017)
  11. Suñé, Víctor; Carrasco, Juan Antonio: Implicit ODE solvers with good local error control for the transient analysis of Markov models (2017)
  12. Tumolo, Giovanni: A mass conservative TR-BDF2 semi-implicit semi-Lagrangian DG discretization of the shallow water equations on general structured meshes of quadrilaterals (2016)
  13. Zupan, E.; Zupan, D.: Velocity-based approach in non-linear dynamics of three-dimensional beams with enforced kinematic compatibility (2016)
  14. Skvortsov, L. M.: Singly implicit diagonally extended Runge-Kutta methods of fourth order (2014)
  15. Dufourd, Claire; Dumont, Yves: Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control (2013)
  16. Heider, Y.; Markert, B.; Ehlers, W.: Dynamic wave propagation in infinite saturated porous media half spaces (2012)
  17. Solin, Pavel; Korous, Lukas: Adaptive higher-order finite element methods for transient PDE problems based on embedded higher-order implicit Runge-Kutta methods (2012)
  18. Wen, Zhiwu; Zhu, Ting; Xiao, Aiguo: Two classes of three-stage diagonally-implicit Runge-Kutta methods with an explicit stage for stiff oscillatory problems (2011)
  19. Markert, B.; Heider, Y.; Ehlers, W.: Comparison of monolithic and splitting solution schemes for dynamic porous media problems (2010)
  20. Bujurke, N. M.; Salimath, C. S.; Shiralashetti, S. C.: Numerical solution of stiff systems from nonlinear dynamics using single-term Haar wavelet series (2008)

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