P
Philippe Chartier
Researcher at French Institute for Research in Computer Science and Automation
Publications - 57
Citations - 1428
Philippe Chartier is an academic researcher from French Institute for Research in Computer Science and Automation. The author has contributed to research in topics: Numerical analysis & Differential equation. The author has an hindex of 24, co-authored 56 publications receiving 1294 citations. Previous affiliations of Philippe Chartier include École normale supérieure de Cachan.
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Algebraic Structures of B-series
TL;DR: This article emphasizes algebraic structures (groups and Hopf algebras of trees) that have recently received much attention also in the non-numerical literature and presents interesting relationships among them.
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Splitting methods with complex times for parabolic equations
TL;DR: In this article, high-order splitting methods with real-time complexity were developed to solve evolution equations posed in finite or infinite dimensional spaces, where complex time steps having positive real part were used to increase the accuracy.
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An Algebraic Approach to Invariant Preserving Integators: The Case of Quadratic and Hamiltonian Invariants
TL;DR: Conditions for the preservation of quadratic and Hamiltonian invariants by numerical methods which can be written as B-series are derived in a purely algebraical way.
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A parallel shooting technique for solving dissipative ODE's
TL;DR: Different modifications of a class of parallel algorithms, initially designed by A. Bellen and M. Zennaro for difference equations and called “across the steps” methods, are studied for the purpose of solving initial value problems in ordinary differential equations on a massively parallel computer.
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Uniformly accurate numerical schemes for highly oscillatory Klein---Gordon and nonlinear Schrödinger equations
TL;DR: In this paper, a general strategy to construct numerical schemes which are uniformly accurate with respect to the oscillation frequency is presented, which enables to simulate the oscillatory problem without using any mesh or time step refinement, and the orders of their schemes are preserved uniformly in all regimes.