About this book
The Green element method (GEM) is a novel approach of implementing in an element-by-element fashion the singular boundary integral theory, thereby enhancing the capabilities of the theory in terms of ease in solving nonlinear problems, adapting to heterogeneous problems, and achieving spareness in the global coefficient matrix. By proceeding in this manner, GEM provides solutions to linear, nonlinear, steady and transient engineering problems in one- and two-dimensional domains, some of which hitherto could not be handled by the boundary integral theory. The primary motivation for the Green element method, therefore, lies in the enhancement of the computational capabilities that it has given to the boundary element theory. The main objectives of this text are to serve as an instructional material to senior undergraduate and first-year graduate students undertaking a course in computational methods and their applications to engineering problems, and as a resource material for research scientists, applied mathematicians, numerical analysts, and engineers who may wish to take these ideas to new frontiers and applications.
Contents
Inflection points, extatic points and curve shortening, S. Angenent; topologically necessary singularities on moving wavefronts and caustics, V.I. Arnold; heteroclinic chains of skew product Hamiltonian systems, S.V. Bolotin; order and chaos in 3-D systems, G. Contopoulos, et al; splitting of separatrices in Hamiltonian systems and symplectic maps, A. Delshams, et al; on the discrete one-dimensional quasi-periodic Schrodinger equation and other smooth quasi-periodic skew products, L.H. Eliasson; Lindstedt series and Kolmogorov theorem, G. Gallavotti; a classical self-contained proof of Kolmogorov's theorem on invariant tori, A. Giorgilli, U. Locatelli; dynamical stability in Lagrangian systems, P. Boyland, C. Gole; the origin of chaotic behaviour in the Kirkwood gaps, J. Henrard; examples of compact hypersurfaces in R2P, 2P >= 6, with no periodic orbits, M. Herman; Hamiltonian systems with three degrees of freedom and hydrodynamics, V.V. Kozlov; introduction to frequency map analysis, J. Laskar; Lindstedt series for lower dimensional tori, A. Jorba, et al; Arnold diffusion - a compendium of remarks and questions, P. Lochak; old and new Applications of Kam theory, J. Moser; on adiabatic invariance in two-frequency systems, A. Neishtadt; the method of rational approximations - theory and applications, J. Seimenis; dynamical systems methods for space missions on a vicinity of collinear libration points, C. Simo; a mechanism of ergodicity in standard-like-maps, Y.G. Sinai; continuous averaging in Hamiltonian systems, D.V. Treschev; phase space geometry and dynamics associated With the 1:2:2 resonance, S. Wiggins; from singular point analysis to rigorous results on integrability - a dream of S. Kowalevskaya, H. Yoshida; contributions time singularities for polynomial Hamiltonians with analytic time dependence, S. Abenda; numerical study of turbulence in N-body Hamiltonian systems with long range force - I. relaxation, M. Antoni, et al; phase space structures in 3 and 4 degrees of freedom - application to chemical reactions, K.M. Atkins, M. Hutson; modulated diffusion for symplectic maps, A. Bazzani, F. Brini; on the Jeans-Landau-Teller approximation for adiabatic invariants, G. Benettin.
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