Marc N.
Spijker 

RESEARCH
Primary research interests
Theoretical numerical analysis  in particular the numerical solution of initial value problems in ordinary and partial differential equations.
Secondary research interests
Parts of classical analysis, matrix theory and operator theory.
Key words related to recent research
Initial value problem, method of lines (MOL), RungeKutta method, linear multistep method, general linear method, ShuOsher representation, totalvariationdiminishing (TVD), totalvariationbounded (TVB), strongstabilitypreserving (SSP), monotonicity, boundedness.
Key words related to some previous research
Initial value problem, discretization, numerical method, RungeKutta formula, linear multistep formula, powers of matrices, power bounded operators, Kreiss matrix theorem, error growth, stability estimate, stability analysis, stability region, resolvent condition, epsilonpseudospectrum.
PUBLICATIONS
General
Publications in scientific journals, proceedings, etc. Click here.
Report on Stability and Boundedness
Report MI201601, Mathematical Institute, Leiden University (2016), "Stability and Boundedness in the Numerical Solution of Initial Value Problems". This is a slightly extended version of a manuscript submitted for publication.
Report on Computing Optimal RungeKutta Methods
Report no. MI200507, Mathematical Institute, Leiden University (2005), written jointly with Luca Ferracina: "Computing optimal monotonicitypreserving RungeKutta methods". There is overlap between Report no. MI 200507 and the paper, written jointly with Luca Ferracina, "Strong stability of singlydiagonallyimplicit RungeKutta methods" (APNUM, 58 (2008) 16751686). But, the report contains material on computing optimal RungeKutta methods which has not been included in the paper.
Lecture Notes "Numerical Stability"
Lecture notes on stability estimates and resolvent conditions in the numerical solution of initial value problems, December 1998, 65 pp. Click here.
Lecture Notes "Inleiding tot de Numerieke Wiskunde"
Lecture notes in Dutch, written jointly with J. A. van de Griend. Introduction to numerical analysis via condition numbers, nonlinear equations, numerical integration, extrapolation techniques, initial value problems, systems of linear and nonlinear equations. April 2008, 103 pp. Click here.
MATHEMATICIANS
WORKING IN RELATED FIELDS
See list
Luca Ferracina
Doctor's thesis (2005): "Monotonicity and boundedness in general RungeKutta methods", can be found via the website of the Mathematical Institute or Leiden University.
NON 
MATHEMATICS
CONTACT
INFORMATION
Address
Department
of Mathematics, Room 205,
Niels Bohrweg 1,
2333 CA
Leiden,
The Netherlands
Phone
+31(0)71527 7138
Fax
+31(0)71527 7101