203 citations · 347 across the 14 of their papers we have counts for
14 papers
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…
Constraints on the magnetic field within a stratified outer core
Colin M Hardy, Philip W Livermore, Jitse Niesen
Mounting evidence from both seismology and experiments on core composition suggests the existence of a layer of stably stratified fluid at the top of Earth's outer core. In this wo…
Three-dimensional solutions for the geostrophic flow in the Earth's core
Colin M. Hardy, Philip W. Livermore, Jitse Niesen +2
In his seminal work, Taylor (1963) argued that the geophysically relevant limit for dynamo action within the outer core is one of negligibly small inertia and viscosity in the magn…
Localized Patterns in Periodically Forced Systems: II. Patterns with Non-Zero Wavenumber
A. S. Alnahdi, J. Niesen, A. M. Rucklidge
In pattern-forming systems, localized patterns are readily found when stable patterns exist at the same parameter values as the stable unpatterned state. Oscillons are spatially lo…
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…
Localized patterns in periodically forced systems
A S Alnahdi, J Niesen, A M Rucklidge +1
Spatially localized, time-periodic structures are common in pattern-forming systems, appearing in fluid mechanics, chemical reactions, and granular media. We examine the existence…
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…
Nonclassical equivalence transformations associated with a parameter identification problem
Nicoleta Bila, Jitse Niesen
A special class of symmetry reductions called nonclassical equivalence transformations is discussed in connection to a class of parameter identification problems represented by par…
Computing stability of multi-dimensional travelling waves
Veerle Ledoux, Simon J. A. Malham, Jitse Niesen +1
We present a numerical method for computing the pure-point spectrum associated with the linear stability of multi-dimensional travelling fronts to parabolic nonlinear systems. Our…
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…
Convergence of the Magnus series
Per Christian Moan, Jitse Niesen
The Magnus series is an infinite series which arises in the study of linear ordinary differential equations. If the series converges, then the matrix exponential of the sum equals…
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…