Toward Non Commutative Numerical Analysis: High Order Integration in Time
Journal of Scientific Computing
Implementation of DIMSIMs for stiff differential systems
Applied Numerical Mathematics
Journal of Scientific Computing
Numerical solution of a problem in the theory of epidemics
Applied Numerical Mathematics - The third international conference on the numerical solutions of volterra and delay equations, May 2004, Tempe, AZ
Nordsieck methods on nonuniform grids: stability and order reduction phenomenon
Mathematics and Computers in Simulation
Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
On quasi-consistent integration by Nordsieck methods
Journal of Computational and Applied Mathematics
General linear methods for ordinary differential equations
Mathematics and Computers in Simulation
Nordsieck representation of two-step Runge--Kutta methods for ordinary differential equations
Applied Numerical Mathematics
Numerical solution of a problem in the theory of epidemics
Applied Numerical Mathematics
Numerical solution of differential-algebraic equations by block methods
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartII
Mathematics and Computers in Simulation
An extension of general linear methods
Numerical Algorithms
Maximal order for second derivative general linear methods with Runge-Kutta stability
Applied Numerical Mathematics
Global Error Control in Adaptive Nordsieck Methods
SIAM Journal on Scientific Computing
Two-step modified collocation methods with structured coefficient matrices
Applied Numerical Mathematics
On the construction of second derivative diagonally implicit multistage integration methods for ODEs
Applied Numerical Mathematics
Construction of algebraically stable DIMSIMs
Journal of Computational and Applied Mathematics
Search for efficient general linear methods for ordinary differential equations
Journal of Computational and Applied Mathematics
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We investigate the implementation of diagonally implicit multistage integration methods (DIMSIMs). The implementation issues addressed are the local error estimation, changing stepsize using the Nordsieck technique, and the construction of continuous interpolants. Numerical experiments with a method of order three indicate that the error estimates that have been constructed are very reliable in both a fixed and a variable stepsize environment.