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 17 articles , 1 standard article )

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  1. 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)
  2. Dufourd, Claire; Dumont, Yves: Impact of environmental factors on mosquito dispersal in the prospect of sterile insect technique control (2013)
  3. Heider, Y.; Markert, B.; Ehlers, W.: Dynamic wave propagation in infinite saturated porous media half spaces (2012)
  4. Solin, Pavel; Korous, Lukas: Adaptive higher-order finite element methods for transient PDE problems based on embedded higher-order implicit Runge-Kutta methods (2012)
  5. 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)
  6. Markert, B.; Heider, Y.; Ehlers, W.: Comparison of monolithic and splitting solution schemes for dynamic porous media problems (2010)
  7. Bujurke, N.M.; Salimath, C.S.; Shiralashetti, S.C.: Numerical solution of stiff systems from nonlinear dynamics using single-term Haar wavelet series (2008)
  8. Sánchez, O.; Herrero, H.; Hoyas, S.; Mucientes, A.E.: Mathematical modeling of Ru(VI)-catalyzed oxidation of alcohols by hexacyanoferrate(III) (2007)
  9. Fijnvandraat, J.G.; Houben, S.H.M.J.; ter Maten, E.J.W.; Peters, J.M.F.: Time domain analog circuit simulation (2006)
  10. Günter, Michael; Feldmann, Uwe; ter Maten, Jan: Modelling and discretization of circuit problems (2005)
  11. Shampine, L.F.; Thompson, S.; Kierzenka, J.A.; Byrne, G.D.: Nonnegative solutions of ODEs (2005)
  12. Allaart-Bruin, Sandra; ter Maten, Jan; Verduyn Lunel, Sjoerd: Modified extended BDF time-integration methods, applied to circuit equations (2004)
  13. Aristizabal, F.; Glavinovič, M.I.: Simulation and parameter estimation of dynamics of synaptic depression (2004)
  14. Alexander, Roger: Design and implementation of DIRK integrators for stiff systems (2003)
  15. Kennedy, Christopher A.; Carpenter, Mark H.: Additive Runge-Kutta schemes for convection-diffusion-reaction equations (2003)
  16. Hosea, M.E.; Shampine, L.F.: Analysis and implementation of TR-BDF2 (1996)
  17. Malhotra, Manish: A computationally efficient technique for transient analysis of repairable Markovian systems (1996)