39 citations · 312 across the 32 of their papers we have counts for
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Integrability of Nonholonomically Coupled Oscillators
Klas Modin, Olivier Verdier
We study a family of nonholonomic mechanical systems. These systems consist of harmonic oscillators coupled through nonholonomic constraints. In particular, the family includes the…
High order semi-Lagrangian methods for the incompressible Navier-Stokes equations
Elena Celledoni, Bawfeh Kingsley Kometa, Olivier Verdier
We propose a class of semi-Lagrangian methods of high approximation order in space and time, based on spectral element space discretizations and exponential integrators of Runge-Ku…
Geometric Generalisations of SHAKE and RATTLE
Robert I. McLachlan, Klas Modin, Olivier Verdier +1
A geometric analysis of the Shake and Rattle methods for constrained Hamiltonian problems is carried out. The study reveals the underlying differential geometric foundation of the…
Reduction and Normal Forms of Matrix Pencils
Olivier Verdier
Matrix pencils, or pairs of matrices, may be used in a variety of applications. In particular, a pair of matrices (E,A) may be interpreted as the differential equation E x' + A x =…
Simplified a priori Estimate for the Time Periodic Burgers' Equation
Magnus Fontes, Olivier Verdier
We present here a version of the existence and uniqueness result of time periodic solutions to the viscous Burgers equation with irregular forcing terms (with Sobolev regularity -1…
Time-Periodic Solutions of the Burgers Equation
Magnus Fontes, Olivier Verdier
We investigate the time periodic solutions to the viscous Burgers equation for irregular forcing terms. We prove that the corresponding Burgers operator i…