Marc N. Spijker
Emeritus
Professor of Numerical Analysis
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Marc N. Spijker |
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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 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
General
Publications in scientific journals, proceedings,
etc. Click here.
Report
on Stepsize-coefficients for Linear Multistep Methods
Report
no. MI-2011-16, Mathematical Institute, Leiden University (2011): “The existence of stepsize-coefficients for boundedness of linear multistep methods”.
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 some 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
See list
Luca Ferracina
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
CONTACT
INFORMATION
Address
Department
of Mathematics, Room 238,
Niels Bohrweg 1,
2333 CA
Leiden,
The Netherlands
Phone
+31(0)71-527 7138
Fax
+31(0)71-527 7101
