203 citations · 347 across the 14 of their papers we have counts for
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New applications for the Boris Spectral Deferred Correction algorithm for plasma simulations
Kris Smedt, Daniel Ruprecht, Jitse Niesen +2
The paper investigates two new use cases for the Boris Spectral Deferred Corrections (Boris-SDC) time integrator for plasma simulations. First, we show that using Boris-SDC as a pa…
Closed-form modified Hamiltonians for integrable numerical integration schemes
Shami A Alsallami, Jitse Niesen, Frank W Nijhoff
Modified Hamiltonians are used in the field of geometric numerical integration to show that symplectic schemes for Hamiltonian systems are accurate over long times. For nonlinear s…
On an asymptotic method for computing the modified energy for symplectic methods
Per Christian Moan, Jitse Niesen
We revisit an algorithm by Skeel et al. for computing the modified, or shadow, energy associated with the symplectic discretization of Hamiltonian systems. By rephrasing the algori…
A Krylov subspace algorithm for evaluating the phi-functions appearing in exponential integrators
Jitse Niesen, Will M. Wright
We develop an algorithm for computing the solution of a large system of linear ordinary differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to computing…
On the global error committed when evaluating the Evans function numerically
Jitse Niesen
The Evans function is a tool for assessing the stability of travelling wave solutions for partial differential equations. A recent paper (math.NA/0605581) analyzes the order reduct…
Evaluating the Evans function: Order reduction in numerical methods
Simon Malham, Jitse Niesen
We consider the numerical evaluation of the Evans function, a Wronskian-like determinant that arises in the study of the stability of travelling waves. Constructing the Evans funct…
A Priori Estimates for the Global Error Committed by Runge-Kutta Methods for a Nonlinear Oscillator
Jitse Niesen
The Alekseev-Gr{ö}bner lemma is combined with the theory of modified equations to obtain an \emph{a priori} estimate for the global error of numerical integrators. This estimate is…