Coarse projective kMC integration: forward/reverse initial and boundary value problems
Journal of Computational Physics
Newton-Krylov continuation of periodic orbits for Navier-Stokes flows
Journal of Computational Physics
Applied Numerical Mathematics
Accelerating an inexact Newton/GMRES scheme by subspace decomposition
Applied Numerical Mathematics
An Analysis of Equivalent Operator Preconditioning for Equation-Free Newton-Krylov Methods
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
A Robust Two-Level Incomplete Factorization for (Navier-)Stokes Saddle Point Matrices
SIAM Journal on Matrix Analysis and Applications
Peer methods with improved embedded sensitivities for parameter-dependent ODEs
Journal of Computational and Applied Mathematics
Reprint of: Peer methods with improved embedded sensitivities for parameter-dependent ODEs
Journal of Computational and Applied Mathematics
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This paper is concerned with the efficient computation of periodic orbits in large-scale dynamical systems that arise after spatial discretization of partial differential equations (PDEs). A hybrid Newton--Picard scheme based on the shooting method is derived, which in its simplest form is the recursive projection method (RPM) of Shroff and Keller [SIAM J. Numer. Anal., 30 (1993), pp. 1099--1120] and is used to compute and determine the stability of both stable and unstable periodic orbits. The number of time integrations needed to obtain a solution is shown to be determined only by the system's dynamics. This contrasts with traditional approaches based on Newton's method, for which the number of time integrations grows with the order of the spatial discretization. Two test examples are given to show the performance of the methods and to illustrate various theoretical points.