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, L.; Rocca, A.Della: Unconditionally strong stability preserving extensions of the TR-BDF2 method (2017)
  2. 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)
  3. Dufourd, Claire; Dumont, Yves: Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control (2013)
  4. Heider, Y.; Markert, B.; Ehlers, W.: Dynamic wave propagation in infinite saturated porous media half spaces (2012)
  5. Solin, Pavel; Korous, Lukas: Adaptive higher-order finite element methods for transient PDE problems based on embedded higher-order implicit Runge-Kutta methods (2012)
  6. 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)
  7. Markert, B.; Heider, Y.; Ehlers, W.: Comparison of monolithic and splitting solution schemes for dynamic porous media problems (2010)
  8. Bujurke, N.M.; Salimath, C.S.; Shiralashetti, S.C.: Numerical solution of stiff systems from nonlinear dynamics using single-term Haar wavelet series (2008)
  9. Sánchez, O.; Herrero, H.; Hoyas, S.; Mucientes, A.E.: Mathematical modeling of Ru(VI)-catalyzed oxidation of alcohols by hexacyanoferrate(III) (2007)
  10. Fijnvandraat, J.G.; Houben, S.H.M.J.; ter Maten, E.J.W.; Peters, J.M.F.: Time domain analog circuit simulation (2006)
  11. Günter, Michael; Feldmann, Uwe; ter Maten, Jan: Modelling and discretization of circuit problems (2005)
  12. Shampine, L.F.; Thompson, S.; Kierzenka, J.A.; Byrne, G.D.: Nonnegative solutions of ODEs (2005)
  13. Allaart-Bruin, Sandra; ter Maten, Jan; Verduyn Lunel, Sjoerd: Modified extended BDF time-integration methods, applied to circuit equations (2004)
  14. Aristizabal, F.; Glavinovič, M.I.: Simulation and parameter estimation of dynamics of synaptic depression (2004)
  15. Alexander, Roger: Design and implementation of DIRK integrators for stiff systems (2003)
  16. Kennedy, Christopher A.; Carpenter, Mark H.: Additive Runge-Kutta schemes for convection-diffusion-reaction equations (2003)
  17. Hosea, M.E.; Shampine, L.F.: Analysis and implementation of TR-BDF2 (1996)
  18. Malhotra, Manish: A computationally efficient technique for transient analysis of repairable Markovian systems (1996)