Marc N. Spijker
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 present research
Initial value problem, method of lines (MOL), Runge-Kutta method, linear multistep method, general linear method, Shu-Osher representation, total-variation-diminishing (TVD), total-variation-bounded (TVB), strong-stability-preserving (SSP), monotonicity, boundedness.
Key words related to some previous research
Initial value problem, discretization, numerical method, Runge-Kutta formula, linear multistep formula, powers of matrices, power bounded operators, Kreiss matrix theorem, error growth, stability estimate, stability analysis, stability region, resolvent condition, epsilon-pseudospectrum.
Publications in scientific journals, proceedings, etc. Click here.
Report on Computing Optimal Runge-Kutta Methods
Report no. MI-2005-07, Mathematical Institute, Leiden University (2005), written jointly with Luca Ferracina: "Computing optimal monotonicity-preserving Runge-Kutta methods". There is overlap between Report no. MI 2005-07 and the paper, written jointly with Luca Ferracina, "Strong stability of singly-diagonally-implicit Runge-Kutta methods" (APNUM, 58 (2008) 1675-1686). But, the report contains material on computing optimal Runge-Kutta 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
Doctor's thesis (2005): "Monotonicity and boundedness in general Runge-Kutta methods", can be found via the website of the Mathematical Institute or Leiden University.
NON - MATHEMATICS
Paintings by Marc Spijker
of Mathematics, Room 238,
Niels Bohrweg 1,
2333 CA Leiden, The Netherlands