/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Preface to the second edition Preface to the first edition 1. Background 2. Orthogonal polynomials in two variables 3. General properties of orthogonal polynomials in several variables 4. Orthogonal polynomials on the unit sphere 5. Examples of orthogonal polynomials in several variables 6. Root systems and Coxeter groups 7. Spherical harmonics associated with reflection groups 8. Generalized classical orthogonal polynomials 9. Summability of orthogonal expansions 10. Orthogonal polynomials associated with symmetric groups 11. Orthogonal polynomials associated with octahedral groups and applications References Author index Symbol index Subject index.

/pdf/orthogonal-polynomials-of-several-variables-2cwkynqk1v.pdf

Orthogonal Polynomials of Several Variables

This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The book is intended as a self consistent treatment of the subject at the graduate level and as a reference for scientists already working in the field. It emphasizes both methods of calculation and results. It is accessible to physicists and engineers without training in modern mathematics. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects. It can be used as a graduate text for a two semester course covering both Hamiltonian and dissipative dynamics.

Regular and Chaotic Dynamics

There are two kinds of tutorial articles: those that provide a primer on an established topic and those that let us in on the ground floor of something of emerging importance. The first type of tutorial can have a noted expert who has been gracious (and brave) enough to write a field guide about a particular topic. The other sort of tutorial typically involves researchers who have each been laboring on a topic for some years. Both sorts of tutorial articles are very much desired. But we, as an editorial board for both Systems and Transactions, know that there has been no logical place for them in the AESS until this series was started several years ago. With these tutorials, we hope to continue to give them a home, a welcome, and provide a service to our membership. We do not intend to publish tutorials on a regular basis, but we hope to deliver them once or twice per year. We need and welcome good, useful tutorial articles (both kinds) in relevant AESS areas. If you, the reader, can offer a topic of interest and an author to write about it, please contact us. Self-nominations are welcome, and even more ideal is a suggestion of an article that the editor(s) can solicit. All articles will be reviewed in detail. Criteria on which they will be judged include their clarity of presentation, relevance, and likely audience, and, of course, their correctness and scientific merit. As to the mathematical level, the articles in this issue are a good guide: in each case the author has striven to explain complicated topics in simple-well, tutorial-terms. There should be no (or very little) novel material: the home for archival science is the Transactions Magazine, and submissions that need to be properly peer reviewed would be rerouted there. Likewise, articles that are interesting and descriptive, but lack significant tutorial content, ought more properly be submitted to the Systems Magazine.

What is a tutorial

https://escholarship.org/content/qt0ck4q6k8/qt0ck4q6k8.pdf?t=li605d

High-Precision Computation: Mathematical Physics and Dynamics

Performance of the Taylor series method for ODEs/DAEs

This paper presents an analysis of the Taylor method for the numerical solution of ODEs when a very high precision of the solution is required. Some theoretical properties of the Taylor method are considered. From the practical point of view a variable-stepsize variable-order (VSVO) scheme is presented and its utility is discussed with several examples. To reach the goal of high precision the use of multiprecision libraries is considered. Finally, some numerical tests based on the test problems given in [1] and on a set of important problems in dynamical systems and astrodynamics are presented showing the benefits of the VSVO formulation, especially for high-precision demands, compared with a well established Runge-Kutta code.

VSVO formulation of the taylor method for the numerical solution of ODEs

Qualitative analysis of the Rössler equations: Bifurcations of limit cycles and chaotic attractors

In this paper we introduce a modification of the fast Lyapunov indicator (FLI) denominated OFLI TT 2 indicator that may provide a global picture of the evolution of a dynamical system. Therefore, it gives an alternative or a complement to the pictures given by the classical Poincare sections and, besides, it may be used for any dimension. We present several examples comparing with the Poincare sections in two classical problems, the Henon–Heiles and the extensible-pendulum problems. Besides, we show the application to Hamiltonians of three degrees of freedom as an isotropic harmonic oscillator in three dimensions perturbed by a cubic potential and non-Hamiltonian problems as a four-dimensional chaotic system. Finally, a numerical method especially designed for its computation is presented in the appendix.

Roberto Barrio

Papers

High-Precision Computation: Mathematical Physics and Dynamics

Performance of the Taylor series method for ODEs/DAEs

VSVO formulation of the taylor method for the numerical solution of ODEs

Qualitative analysis of the Rössler equations: Bifurcations of limit cycles and chaotic attractors

Sensitivity tools vs. Poincaré sections