Articles Willem Hundsdorfer

Journals

• W. Hundsdorfer, A. Mozartova and M. N. Spijker,
  Stepsize Restrictions for Boundedness and Monotonicity of Multistep Methods,
  J. Sci. Comput. 50 (2012), 265-286.
  

• Chao Li, U. Ebert, W. Hundsdorfer,
  Spatially hybrid computations for streamer discharges: II. Fully 3D simulations,
  J. Comput. Phys. 231 (2012), 1020-1050.
  

• W. Hundsdorfer, A. Mozartova and M. N. Spijker,
  Special boundedness properties in numerical initial value problems,
  BIT Numer, Math, 51 (2011), 909-936.
  

• Chao Li, U. Ebert, W. Hundsdorfer,
  Simulated avalanche formation around streamers in an overvolted air gap,
  IEEE Trans. Plasma Sci. 39 (2011), 2256-2257.
  

• U. Ebert, F. Brau, G. Derks, W. Hundsdorfer, C.-Y. Kao, C. Li, A. Luque,
  B. Meulenbroek, S. Nijdam, V. Ratushnaya, L. Schäfer, S. Tanveer,
  Multiple scales in streamer discharges, with an emphasis on moving boundary approximations,
  Nonlinearity 24 (2011), C1-C26.
  

• C. Li, U. Ebert, W. Hundsdorfer,
  Spatially hybrid computations for streamer discharges with generic features of pulled fronts: I. Planar fronts,
  J. Comput. Phys. 229 (2010), 200-220.
  

• W. Hundsdorfer, A. Mozartova, M.N. Spijker,
  Stepsize Conditions for Boundedness in Numerical Initial Value Problems,
  Siam J. Numer. Anal. 47 (2009), 3797-3819.
  

• W. Hundsdorfer, V. Savcenco,
  Analysis of a multirate theta-method for stiff ODEs,
  Appl. Num. Math. 59 (2009), 693-706.
  

  C. Li, U. Ebert, W. Hundsdorfer,
  3D hybrid computations for streamer discharges and production of run-away electrons,
  J. Phys. D: Appl. Phys. 42, 202003 (5p) (2009).
  

• A. Luque, U. Ebert, W. Hundsdorfer,
  Interaction of streamer discharges in air and other oxygen-nitrogen mixtures,
  Phys. Rev. Lett. 101, 075005 (2008).
  

• W. Hundsdorfer, S.J. Ruuth,
  IMEX extensions of linear multistep methods with general monotonicity and boundedness properties,
  J. Comput. Phys. 225 (2007), 2016--2042.
  

• V. Savcenco, W. Hundsdorfer, J.G. Verwer,
  A Multirate Time Stepping Strategy for Stiff ODEs,
  BIT Numer. Math. 47 (2007), 137--155.
  

• W. Hundsdorfer, L. Portero,
  A Note on Iterated Splitting Schemes,
  J. Comp. Appl. Math. 201 (2007), 146--152.
  

• A. Luque, U. Ebert, C. Montijn, W. Hundsdorfer,
  Photoionisation in negative streamers: fast computations and two propagation modes,
  Appl. Phys. Lett. 90, 081501 (2007).
  

• C. Montijn, W. Hundsdorfer, U. Ebert,
  An adaptive grid refinement strategy for the simulation of negative streamers,
  J. Comput. Phys. 219 (2006), 801--835.
  

• N.N. Pham Thi, W. Hundsdorfer, B.P. Sommeijer,
  Positivity for explicit two-step methods in linear multistep and one-leg form,
  BIT Numer. Math. 46 (2006), 875--882.
  

• W. Hundsdorfer, S.J. Ruuth,
  On monotonicity and boundedness properties of linear multistep methods,
  Math. Comp. 75 (2006), 655--672.
  

• C. Montijn, U. Ebert, W. Hundsdorfer,
  Numerical convergence of the branching time of negative streamers,
  Phys. Rev. E 73, 065401 (2006)
  

• U. Ebert, C. Montijn, T.M.P. Briels, W. Hundsdorfer, B. Meulenbroek, A. Rocco, E.M. van Veldhuizen,
  The multiscale nature of streamers,
  Plasma Sources Science and Technology 15 (2006), S118--S129.
  

• S.J. Ruuth, W. Hundsdorfer,
  High-order linear multistep methods with general monotonicity and boundedness properties,
  J. Comput. Phys. 209 (2005), 226--248.
  

• C. Montijn, B. Meulenbroek, U. Ebert, W. Hundsdorfer,
  Numerical simulations and conformal mapping analysis of growing and branching negative discharge streamers,
  IEEE Trans. Plasma Sci. 33 (2005), 260--261.
  

• J.G. Verwer, B.P. Sommeijer, W. Hundsdorfer,
  RKC Time-Stepping for Advection-Diffusion-Reaction Problems,
  J. Comput. Phys. 201 (2004), 61--79.
  

• W. Hundsdorfer, C. Montijn,
  A Note on Flux Limiting for Diffusion equations,
  IMA J. Numer. Anal. 24 (2004), 635--642.
  

• W. Hundsdorfer , S.J. Ruuth , R.J. Spiteri ,
  Monotonicity-preserving linear multistep methods,
  SIAM J. Num. Anal. 41 (2003), 605--623.
  

• W. Hundsdorfer , J. Jaffré ,
  Implicit-Explicit Time Stepping with Spatial Discontinuous Finite Elements,
  Appl. Num. Math. 45 (2003), 231--254.
  

• W. Hundsdorfer ,
  Accuracy and stability of splitting with Stabilizing Corrections,
  Appl. Num. Math. 42 (2002), 213--233.
  

• A. Rocco, U. Ebert, W. Hundsdorfer,
  Branching of negative streamers in free flight,
  Phys. Rev. E 66, 035102(R) (2002).
  

• P. Rodin, U. Ebert, W. Hundsdorfer, I.V. Grekhov,
  Superfast fronts of impact ionization in initially unbiased layered semiconductor structures
  J. Appl. Phys. 92 (2002), 1971--1980.
  

• P. Rodin, U. Ebert, W. Hundsdorfer, I.V. Grekhov,
  Tunneling-assisted impact ionization fronts in semiconductors,
  J. Appl. Phys. 92 (2002), 958--964.
  

• J.G. Verwer, W. Hundsdorfer , J.G. Blom,
  Numerical time integration for air pollution models,
  Surveys Math. Indust. 10 (2002), 107--174.
  

• M. Arrays, U. Ebert, W. Hundsdorfer,
  Spontaneous branching of anode-directed streamers between planar electrodes,
  Phys. Rev. Lett. 88, 174502 (2002).
  

• W. Hundsdorfer ,
  Partially implicit BDF2 blends for convection dominated flows,
  SIAM J. Num. Anal. 38 (2001), 1763--1783.
  

• J.G. Verwer, E.J. Spee, J.G. Blom, W. Hundsdorfer ,
  A second order Rosenbrock method applied to photochemical dispersion problems,
  SIAM J. Sci. Comput. 20 (1999), 1456--1480.
  

• W. Hundsdorfer ,
  Stability of approximate factorization with $\theta$-methods,
  BIT 39 (1999), 473--483.
  

• E.J. Spee, A.C. Petersen, H. van Dop, W. Hundsdorfer ,
  Sensitivity of atmospheric transport model performance to numerical advection schemes and resolution,
  J. Geophys. Res. 103 (1998), 19,253--19,269.
  

• E.J. Spee, J.G. Verwer, P.M. de Zeeuw, J.G. Blom, W. Hundsdorfer ,
  A numerical study for global atmospheric transport-chemistry problems,
  Mathematics and Computers in Simulation 48 (1998), 177--204.
  

• W. Hundsdorfer ,
  A note on stability of the Douglas splitting method,
  Math. Comp. 67 (1998), 183--190.
  

• W. Hundsdorfer ,
  Trapezoidal and midpoint splittings for initial-boundary value problems
  Math. Comp. 67 (1998), 1047--1062.
  

• J. Frank, W. Hundsdorfer J.G. Verwer,
  On the stability of implicit-explicit linear multistep methods,
  Appl. Num. Math. 25 (1997), 193--205.
  

• J.G. Verwer, J.G. Blom, W. Hundsdorfer ,
  An implicit-explicit approach for atmospheric transport-chemistry problems,
  Appl. Num. Math. 20 (1996), 191--209.
  

• W. Hundsdorfer , E.J. Spee,
  An efficient horizontal advection scheme for the modelling of global transport of constituents,
  Mon. Wea. Rev. 123 (1995), 3554--3564.
  

• W. Hundsdorfer , B. Koren, M. van Loon, J.G. Verwer,
  A positive finite-difference advection scheme,
  J. Comput. Phys. 117 (1995), 35--46.
  

• W. Hundsdorfer , J.G. Verwer,
  A note on splitting errors for advection-reaction equations,
  Appl. Num. Math. 18 (1995), 191--199.
  

• J.L.M. van Dorsselaer, W. Hundsdorfer ,
  Stability estimates based on numerical ranges with an application to a spectral method,
  BIT 34 (1994), 228--238.
  

• W. Hundsdorfer , R.A. Trompert,
  Method of lines and direct discretization: a comparison for linear advection,
  Appl. Numer. Math. 13 (1994), 469--490.
  

• W. Hundsdorfer ,
  On the error of general linear methods for stiff dissipative differential equations,
  IMA J. Numer. Anal. 14 (1994), 363--379.
  

• W. Hundsdorfer ,
  Unconditional convergence of some Crank-Nicolson LOD methods for initial-boundary value problems,
  Math. Comp. 58 (1992), 35--53.
  

• W.H. Hundsdorfer , B.I. Steininger,
  Convergence of linear multistep and one-leg methods for stiff nonlinear initial value problems,
  BIT 31 (1991), 124--143.
  

• J.G. Verwer, W.H. Hundsdorfer, B.P. Sommeijer,
  Convergence of the Runge-Kutta-Chebyshev method ,
  Numer. Math. 57 (1990), 157--178.
  

• W.H. Hundsdorfer , J. Schneid,
  An algebraic characterization of B-convergent Runge-Kutta methods,
  Numer. Math. 56 (1990), 695--705.
  

• W.H. Hundsdorfer , J. Schneid,
  On the equivalence of BS-stability and B-convergence,
  BIT 29 (1989), 505--511.
  

• W.H. Hundsdorfer , J.G.Verwer,
  Stability and convergence of the Peaceman-Rachford ADI method for initial-boundary value problems,
  Math. Comp. 53 (1989), 81--101.
  

• W.H. Hundsdorfer , J.G. Verwer,
  Linear stability of the Hopscotch scheme,
  Appl. Numer. Math. 5 (1989), 423--433.
  

• W.H. Hundsdorfer ,
  A note on monotonicity of a Rosenbrock method,
  J. Comp. Appl. Math. 20 (1987), 267--273.
  

• W.H. Hundsdorfer , M.N. Spijker,
  On the algebraic equations in implicit Runge-Kutta methods,
  SIAM J. Numer. Anal. 24 (1987), 583--594.
  

• K. Burrage, W.H. Hundsdorfer ,
  The order of B-convergence of algebraically stable Runge-Kutta methods,
  BIT 27 (1987), 62--71.
  

• J.M. Sanz-Serna, J.G.Verwer, W.H. Hundsdorfer ,
  Convergence and order reduction of Runge-Kutta schemes applied to evolutionary problems in partial differential equations,
  Numer. Math. 50 (1987), 405--418.
  

• W.H. Hundsdorfer ,
  Stability and B-convergence of linearly implicit Runge-Kutta methods,
  Numer. Math. 50 (1986), 83--95.
  

• K. Burrage, W.H. Hundsdorfer, J.G. Verwer,
  A study of B-convergence of Runge-Kutta methods,
  Computing 36 (1986), 17--34.
  

• W.H. Hundsdorfer ,
  The Numerical Solution of Stiff Initial Value Problems -- an analysis of one-step methods,
  CWI Tract 12, Amsterdam 1985. Reprint of PhD thesis.
  

• M. Crouzeix, W.H. Hundsdorfer, M.N. Spijker,
  On the existence of solutions to the algebraic equations in implicit Runge-Kutta methods,
  BIT 23 (1983), 84--91.
  

• W.H. Hundsdorfer , M.N. Spijker,
  A note on B-stability of Runge-Kutta methods,
  Numer. Math. 36 (1981), 319--332.
  

Proceedings and Technical Reports

• C. Montijn, U. Ebert, W. Hundsdorfer, Adaptive grid simulations of negative streamers in nitrogen in under- and overvolted gaps,
  Refereed proceedings of the XXVII'th ICPIG 2005.

• W. Hundsdorfer, S.J. Ruuth,
  Monotonicity for Time Discretizations,
  Procs. Dundee Conference 2003, Eds. D.F. Griffiths, G.A. Watson,
  Report NA/217, Univ. of Dundee, 2003.

• P. Rodin, U. Ebert, W. Hundsdorfer, I.V. Grekhov, A novel type of power picosecond semiconductor switches based on tunneling-assisted impact ionization fronts, Conference Record 25th Int. Power Modulator Symposium, 2002 and 2002 High Voltage Workshop (ISSN: 1076-8467), pp. 445-448.

• U. Ebert, A. Rocco, W. Hundsdorfer, M. Arrayás, A mechanism for streamer branching, 2 pages in: 16th ESCAMPIG and 5th ICRP Joint Conference, Grenoble, July 2002.

• W. Hundsdorfer , E.J. Spee, An atmospheric test model for global advection and chemistry, Proceedings ICIAM95, ZAMM, Issue 4: Applied Sciences - Mechanics, pp. 442-443. Akademie Verlag, 1996.

• W. Hundsdorfer, Numerical Solution of Advection-Diffusion-Reaction Equations, Lecture Notes, CWI Note NM-N9603, Amsterdam, 1996.

• E.J. Spee, P.M. de Zeeuw, Verwer, J.G. Blom, W. Hundsdorfer , Vectorization and parallelization of a numerical scheme for 3D global atmospheric transport-chemistry problems, CRAY-NCF project, CWI Report NM-R9620, Amsterdam 1996.

• J.G. Blom, W. Hundsdorfer , J.G. Verwer, Vectorization aspects of a spherical advection scheme on a reduced grid, CRAY-NCF project, CWI Report NM-R9418, Amsterdam 1994.

• J.G. Verwer, W.H. Hundsdorfer, B.P. Sommeijer, Convergence properties of the Runge-Kutta-Chebyshev method, Numerical treatment of differential equations (Halle, 1989), 273-284, K. Strehmel (ed.), Teubner-Texte Math., 121, Teubner, Stuttgart, 1991

• W. Hundsdorfer, Local and global order reduction of some LOD schemes, Numerical treatment of differential equations (Halle, 1989), 225-232, K. Strehmel (ed.), Teubner-Texte Math., 121, Teubner, Stuttgart, 1991.

• K. Strehmel, W.H. Hundsdorfer, R. Weiner, M. Arnold, The linearly implicit Euler method for quasi-linear parabolic differential equations, CWI Report NM-R9002, Amsterdam 1990.

• W.H. Hundsdorfer, Convergence of Runge-Kutta methods on classes of stiff initial value problems, Proceedings Int. Congress Numer. Anal., B. Karasozen (ed.), METU, Ankara 1989.

• W.H. Hundsdorfer, Stability results for $theta$-methods applied to a class of stiff differential algebraic equations, CWI Report NM-R8708, Amsterdam, 1987.

• B.P. Sommeijer, W.H. Hundsdorfer , K. Everaars, P.J. van der Houwen and J.G. Verwer, A numerical study of a 1-D stationary semi-conductor model, CWI Note NM-N8702, Amsterdam, 1987.

• W.H. Hundsdorfer, B.P. Sommeijer, J.G. Verwer, A numerical study of a 1-D scalar semi-conductor model equation, CWI Note NM-N8602, Amsterdam, 1986.

• W.H. Hundsdorfer, Nonlinear stability analysis of a simple Rosenbrock method, Report 81-31, Inst. Appl. Math., Univ. Leiden, 1981.