galepu swMATH ID: 15103 Software Authors: Gameiro, Marcio; Lessard, Jean-Philippe; Pugliese, Alessandro Description: Computation of smooth manifolds via rigorous multi-parameter continuation in infinite dimensions. In this paper, we introduce a constructive rigorous numerical method to compute smooth manifolds implicitly defined by infinite-dimensional nonlinear operators. We compute a simplicial triangulation of the manifold using a multi-parameter continuation method on a finite-dimensional projection. The triangulation is then used to construct local charts and an atlas of the manifold in the infinite-dimensional domain of the operator. The idea behind the construction of the smooth charts is to use the radii polynomial approach to verify the hypotheses of the uniform contraction principle over a simplex. The construction of the manifold is globalized by proving smoothness along the edge of adjacent simplices. We apply the method to compute portions of a two-dimensional manifold of equilibria of the Cahn-Hilliard equation. Homepage: http://archimede.mat.ulaval.ca/jplessard/galepu/ Dependencies: Matlab; intlab Keywords: continuation; simplicial approximation; triangulation; contraction mapping; rigorous numerics Related Software: INTLAB; MATCONT; Matlab; AUTO; CL_MATCONT; GitHub; RODES; Taylor; CkAnalytic; COCO; XPPAUT; DISODE45; SlideCont; DifferentialEquations.jl; NeuralPDE.jl; Julia; DPCM; HomCont; CAPD; PyDSTool Cited in: 15 Publications all top 5 Cited by 24 Authors 6 Lessard, Jean-Philippe 5 Mireles-James, Jason D. 3 van den Berg, Jan Bouwe 2 Breden, Maxime 2 Pugliese, Alessandro 2 Queirolo, Elena 1 Capinski, Maciej J. 1 Chainais-Hillairet, Claire 1 Church, Kevin E. M. 1 Colombo, Alessandro G. 1 Cyranka, Jacek 1 de la Llave, Rafael 1 Del Buono, Nicoletta 1 Gameiro, Marcio F. 1 Hénot, Olivier 1 Hetebrij, Wouter 1 Hungria, Allan 1 Kühn, Christian 1 Lappicy, Phillipo 1 Lopez, Luciano 1 Ransford, Julian 1 Sprink, Hauke 1 Wanner, Thomas 1 Zurek, Antoine all top 5 Cited in 11 Serials 4 SIAM Journal on Applied Dynamical Systems 1 General Relativity and Gravitation 1 Nonlinearity 1 Mathematics of Computation 1 Physica D 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Celestial Mechanics and Dynamical Astronomy 1 Foundations of Computational Mathematics 1 Discrete and Continuous Dynamical Systems. Series B 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Journal of Computational Dynamics all top 5 Cited in 14 Fields 12 Numerical analysis (65-XX) 8 Ordinary differential equations (34-XX) 6 Dynamical systems and ergodic theory (37-XX) 4 Partial differential equations (35-XX) 2 Operator theory (47-XX) 2 Computer science (68-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Approximations and expansions (41-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year