Publications by M.N. Spijker in journals, proceedings etc.

• “Stability and boundedness in the numerical solution of initial value problems”
  Math. Comp. 86, 2777-2798 (2017).

• ''The existence of stepsize-coefficients for boundedness of linear multistep methods''
  Appl. Numer. Mathem. 63, 45-57 (2013).

•  "Stepsize restrictions for boundedness and monotonicity of multistep methods''
  (joint autors W.Hundsdorfer, A.Mozartova)
  Journ. Sci. Comput. 50, 265-286 (2012). 

•  "Special boundedness properties in numerical initial value problems''
  (joint autors W.Hundsdorfer, A.Mozartova)
  BIT Numerical Mathematics 51, 909-936 (2011). 

•  "Boundedness and strong stability of Runge-Kutta methods''
  (joint autor W.Hundsdorfer)
  Math. Comp. 80, 863-886 (2011). 

•  ''Stepsize conditions for boundedness in numerical initial value problems'',
  (joint authors W.Hundsdorfer, A.Mozartova),
  SIAM J. Numer. Anal. 47, 3797-3819 (2009). 

•  "Strong stability of singly-diagonally-implicit Runge-Kutta methods"
  (joint autor L.Ferracina),
  Appl. Numer. Mathem. 58, 1675-1686 (2008). 

•  "Stepsize conditions for general monotonicity in numerical initial value problems ",
  SIAM J. Numer. Anal. 45, 1226-1245 (2007). 

•  "Stepsize restrictions for total-variation-boundedness in general Runge-Kutta procedures"
  (joint autor L.Ferracina),
  Appl. Numer. Mathem. 53, 265-279 (2005). 

•  "An extension and analysis of the Shu-Osher representation of Runge-Kutta methods"
  (joint author L.Ferracina),
  Math. Comp. 74, 201-219 (2005). 

• "Stepsize restrictions for the total-variation-diminishing property in general Runge-Kutta methods"
  (joint author L.Ferracina),
  SIAM J. Numer. Anal. 42, 1073-1093 (2004).

• "Analysis of error growth via stability regions in numerical initial value problems"
  (joint author K.J.in 't Hout),
  BIT 43, 363-385 (2003).

• "About the sharpness of the stability estimates in the Kreiss matrix theorem"
  (joint authors S.Tracogna, B.D.Welfert),
  Math. Comp. 72, 697-713 (2003).

• "Bounding partial sums of Fourier series in weighted L2-norms, with applications to matrix analysis"
  (joint author N.Borovykh),
  Journ. Comp. Appl. Math. 147, 349-368 (2002).

• "A bound on powers of linear operators, with relevance to numerical stability"
  (joint authors N.Borovykh, D.Drissi),
  Applied Mathematics Letters 15, 47-53 (2002).

•  "Resolvent conditions and bounds on the powers of matrices, with relevance to numerical stability of initial value problems"
  (joint author N. Borovykh),
  Journ. Comp. Appl. Math. 125, 41-56 (2000).

• "The sharpness of stability estimates corresponding to a general resolvent condition"
  (joint author N. Borovykh),
  Linear Algebra Appl. 311, 161-175 (2000).

• "A note about Ritt's condition, related resolvent conditions, and power bounded operators"
  (joint authors N. Borovykh, D. Drissi),
  Numer. Function. Anal. Optimiz. 21, 425-438 (2000).

• "A note on the order of contact between sets in the complex plane",
  (joint author F.A.J. Straetemans),
  Journ. Mathem. Anal. Applic. 217, p. 707-723 (1998).

• "Numerical stability, resolvent conditions and delay differential equations",
  Appl. Numer. Mathem. 24, p. 233-246 (1997).

• "Error growth analysis via stability regions for discretizations of initial value problems"
  (joint author F.A.J. Straetemans),
  BIT 37, p. 442-464 (1997).

• "Error propagation in Runge-Kutta methods",
  Appl. Numer. Mathem. 22, p. 309-325 (1996).

• "The effect of stopping Newton-type iterations in implicit linear multistep methods",
  CWI Quarterly 9, p. 137-142 (1996).

•  "Stiffness in numerical initial-value problems",
  Journ. Comp. Appl. Math. 72, p. 393-406 (1996).

• "Stability estimates for families of matrices of nonuniformly bounded order"
  (joint author F.A.J. Straetemans),
  Linear Algebra Appl. 239, p. 77-102 (1996).

• "The effect of the stopping of the Newton iteration in implicit linear multistep methods",
  Appl. Numer. Mathem. 18, p. 367-386 (1995).

• "On the error committed by stopping the Newton iteration in implicit Runge-Kutta methods" Annals of Numer. Mathem. 1, p. 199-212 (1994).

• "On the error due to the stopping of the Newton iteration in implicit linear multistep methods"
  (joint author J. Groeneweg),
  Numerical analysis 1993, Proceedings of the 15th Dundee Conference, (D.F. Griffiths & G.A. Watson,eds.), p. 157-166. Harlow: Longman Scientific & Technical (1994).

• "The error committed by stopping the Newton iteration in the numerical solution of stiff initial value problems".
  (joint author J.L.M. van Dorsselaer),
  IMA Journ. Numer. Anal. 14, p. 183-209 (1994).

• "About stability estimates and resolvent conditions"
  (joint authors J.L.M. van Dorsselaer, J.F.B.M. Kraaijevanger),
  Numerical Analysis and Mathematical Modelling, p. 215-225. (Banach Center Publications, vol. 29) Inst. Math., Pol. Ac. Sc., Warszawa (1994).

•  "Numerical ranges and stability estimates",
  Appl. Numer. Mathem. 13, p. 241-249 (1993). 

• "Linear stability analysis in the numerical solution of initial value problems",
  (joint authors J.L.M. van Dorsselaer, J.F.B.M. Kraaijevanger),
  Acta Numerica 1993, p. 199-237 (1993).

• "Stability criteria in the numerical solution of initial value problems",
  Computational ordinary differential equations (J.R. Cash & I.~Gladwell, eds.), p. 19-27. (Conference Series of the Institute of Mathematics and its Applications, nr. 39)
  Oxford: University Press (1992).

• "The theta-methods in the numerical solution of delay differential equations".
  (joint author K.J. in 't Hout),
  The Numerical treatment of differential equations,
  (K. Strehmel, ed.), p. 61-67. (Teubner-Texte zur Mathematik, Band 121) Stuttgart: B.G. Teubner Verlagsgesellschaft (1991).

• "On the use of stability regions in the numerical analysis of initial value problems".
  (joint author H.W.J. Lenferink),
  Math. Comp. 57, p. 221-237 (1991).

• "On a generalization of the resolvent condition in the Kreiss matrix theorem".
  (joint author H.W.J. Lenferink),
  Math. Comp. 57, p. 211-220 (1991).

• "Stability analysis of numerical methods for delay differential equations".
  (joint author K.J. in 't Hout),
  Numer. Math. 59, p. 807-814 (1991).

• "On a conjecture by LeVeque and Trefethen related to the Kreiss matrix theorem".
  BIT 31, p. 551-555 (1991).

• "A generalization of the numerical range of a matrix".
  (joint author H.W.J. Lenferink),
  Linear Algebra Appl. 140, p. 251-266 (1990).

• "The stability of the theta-methods in the numerical solution of delay differential equations".
  (joint author M.Z. Liu),
  IMA Journ. Numer. Anal. 10, p. 31-48 (1990).

• "Algebraic stability and error propagation in Runge-Kutta methods".
  (joint author J.F.B.M. Kraaijevanger),
  Appl. Numer. Mathem. 5, p. 71-87 (1989).

• "The relevance of stability regions in the numerical solution of initial value problems".
  (joint author H.W.J. Lenferink),
  Numerical Treatment of Differential Equations, (K. Strehmel, ed.), p. 95-103. (Teubner Texte zur Mathematik, Band 104) Leipzig: Teubner Verlag (1988).

• "Monotonicity and contractivity phenomena in the numerical solution of stiff differential equations'.
  Discretization in differential equations and enclosures,
  eds. E. Adams, R. Ansorge, C. Grossmann, H-G Roos, Mathematical Research Band 36, p. 207-218. Berlin: Akademie-Verlag (1987).

• "Suitability of Runge-Kutta methods".
  (joint authors M.Z. Liu, K. Dekker),
  Journ. Comp. Appl. Math. 20, p. 307-316 (1987).

• "Stepsize restrictions for stability in the numerical solution of ordinary and partial differential equations".
  (joint authors J.F.B.M. Kraaijevanger, H.W.J. Lenferink),
  Journ. Comp. Appl. Math. 20, p. 67-81 (1987).

• "A note on contractivity in the numerical solution of initial value problems".
  BIT 27, p. 424-437 (1987).

• "On the algebraic equations in implicit Runge-Kutta methods".
  (joint author W.H. Hundsdorfer),
  SIAM Journal on Numer. Anal. 24, p. 583-594 (1987).

• "Monotonicity and boundedness in implicit Runge-Kutta methods".
  Numer. Math. 50, p. 97-109 (1986).

• "The Relevance of algebraic stability in implicit Runge-Kutta methods".
  Numerical Treatment of Differential Equations, (K. Strehmel, ed.), p. 158-164.
  Leipzig: Teubner Verlagsgesellschaft (1986).

• "Regions of stability, Equivalence Theorems and the Courant-Friedrichs-Lewy Condition".
  (joint author J.M. Sanz-Serna),
  Numer. Math. 49, p. 319-329 (1986).

• "The order of B-convergence of the Gaussian Runge-Kutta method".
  (joint authors K. Dekker, J.F.B.M. Kraaijevanger),
  Computing 36, p. 35-41 (1986).

• "Stepsize restrictions for stability of one-step methods in the numerical solution of initial value problems".
  Math. Comp. 45, p. 377-392 (1985).

• "Feasibility and contractivity in implicit Runge-Kutta methods".
  Journ. Comp. Appl. Math. 12 & 13, p. 563-578 (1985).

• "Numerical contractivity in the solution of initial value problems".
  Numerische Behandlung von Differentialgleichungen (K. Strehmel, ed.), p. 118-124. Halle-Wittenberg (1984).

• "On the relation between stability and contractivity".
  BIT 24, p. 656-666 (1984).

• "Contractivity in the numerical solution of initial value problems".
  Numer. Math. 42, p. 271-290 (1983).

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

• "Stability in the numerical solution of stiff initial value problems".
  Nieuw Archief voor Wiskunde 30, p. 264-276 (1982).

• "Contractivity of Runge-Kutta methods".
  Numerical methods for solving stiff initial value problems (eds. G. Dahlquist, R. Jeltsch).
  Bericht Nr. 9, Inst. Geom. Prakt. Math. RWTH Aachen, Proceedings Oberwolfach Conference, 4 p. (1981).

• "Stability concepts for discretization methods".
  Proceedings Mathematiker-Kongress DDR 1981, p. 129-134, Leipzig: Karl Marx Universität (1981).

• "A note on B-stability of Runge-Kutta methods".
  (joint author W.H. Hundsdorfer),
  Numer. Math. 36, p. 319-331 (1981).

• "On two-sided error bounds for Runge-Kutta methods".
  Tagungsreihe der Wissenschaftlichen Zeitschrift der Technischen Hochschule Karl-Marx-Stadt. 7.TMP, p. 81-87 (1979).

• "Error bounds in the numerical solution of initial value problems".
  Proceedings of the Bicentennial of the Wiskundig Genootschap,
  M.C. Tract 101, p. 345-358. Amsterdam: Mathematisch Centrum (1978).

• "The behaviour of error bounds in the numerical solution of initial value problems when the stepsize h tends to zero".
  Topics in Numerical Analysis III (J.J.H. Miller, ed.), p. 383-400.
  London: Academic Press (1977).

• "On the possibility of two-sided error bounds in the numerical solution of initial value problems".
  Numer. Math. 26, p. 271-300 (1976).

• "Two-sided error estimates in the numerical solution of initial value problems".
  Lecture Notes in Mathematics no. 395, p. 109-122, Springer Verlag (1974).

• "Optimum error estimates for finite-difference methods".
  Acta Universitatis Carolinae-Mathematica et Physica 15, p. 159-164 (1974).

• "Equivalence theorems for nonlinear finite-difference methods".
  Lecture Notes in Mathematics no. 267, p. 233-266, Springer Verlag (1972).

• "On the structure of error estimates for finite-difference methods". Numer. Math. 18, p. 73-100 (1971).

• "Reduction of roundoff error by splitting of difference formulas".
  SIAM J. Numer. Anal. 8, p. 345-357 (1971).

• "Superposition in linear and nonlinear ordinary differential equations"
  J. Math. Anal. Appl. 30, p. 206-222 (1970).

• "Round-off error in the numerical solution of second order differential equations".
  Lecture Notes in Mathematics no. 109, p. 249-254, Springer Verlag (1969).

• "Stability and convergence of finite-difference methods".
  Doctor's Thesis, Leiden University (1968).

• "Behoud van stabiliteit bij wijziging van een differentieschema".
  Colloquium Stabiliteit van differentie-schema's,
  M.C. Syllabus 2.2, p. 42-49, Amsterdam: Mathematisch Centrum (1968).

• "On the consistency of finite-difference methods for the solution of initial value problems".
  J. Math. Anal. App.19, p. 125-132 (1967).

• "Convergence and stability of step-by-step methods for the numerical solution of initial-value problems".
  Numer. Math. 8, p. 161-177 (1966).