TR-BDF2

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.


References in zbMATH (referenced in 36 articles , 1 standard article )

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  1. Dumont, Y.; Yatat-Djeumen, I. V.: Sterile insect technique with accidental releases of sterile females: impact on mosquito-borne diseases control when viruses are circulating (2022)
  2. Garres-Díaz, J.; Fernández-Nieto, E. D.; Narbona-Reina, G.: A semi-implicit approach for sediment transport models with gravitational effects (2022)
  3. Bonaventura, Luca; Mármol, Macarena Gómez: The TR-BDF2 method for second order problems in structural mechanics (2021)
  4. Capera-Aragones, Pau; Foxall, Eric; Tyson, Rebecca C.: Differential equation model for central-place foragers with memory: implications for bumble bee crop pollination (2021)
  5. Garres-Díaz, José; Bonaventura, Luca: Flexible and efficient discretizations of multilayer models with variable density (2021)
  6. Wu, Shu-Lin; Zhou, Tao: Parallel implementation for the two-stage SDIRK methods via diagonalization (2021)
  7. Bonaventura, Luca; Casella, F.; Carciopolo, L. Delpopolo; Ranade, A.: A self adjusting multirate algorithm for robust time discretization of partial differential equations (2020)
  8. 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)
  9. Delpopolo Carciopolo, Ludovica; Bonaventura, Luca; Scotti, Anna; Formaggia, Luca: A conservative implicit multirate method for hyperbolic problems (2019)
  10. De Oliveira Vilaca, Luis Miguel; Milinkovitch, Michel C.; Ruiz-Baier, Ricardo: Numerical approximation of a 3D mechanochemical interface model for skin patterning (2019)
  11. 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)
  12. Boom, Pieter D.; Zingg, David W.: Optimization of high-order diagonally-implicit Runge-Kutta methods (2018)
  13. Perchikov, Nathan; Gendelman, O. V.: Transient dynamics in strongly nonlinear systems: optimization of initial conditions on the resonant manifold (2018)
  14. Anguelov, Roumen; Dufourd, Claire; Dumont, Yves: Mathematical model for pest-insect control using mating disruption and trapping (2017)
  15. Bonaventura, L.; Della Rocca, A.: Unconditionally strong stability preserving extensions of the TR-BDF2 method (2017)
  16. Owhadi, Houman; Zhang, Lei: Gamblets for opening the complexity-bottleneck of implicit schemes for hyperbolic and parabolic ODEs/PDEs with rough coefficients (2017)
  17. Suñé, Víctor; Carrasco, Juan Antonio: Implicit ODE solvers with good local error control for the transient analysis of Markov models (2017)
  18. 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)
  19. Zupan, E.; Zupan, D.: Velocity-based approach in non-linear dynamics of three-dimensional beams with enforced kinematic compatibility (2016)
  20. Skvortsov, L. M.: Singly implicit diagonally extended Runge-Kutta methods of fourth order (2014)

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