Computer algebra in scientific computing : CASC 2001 : proceedings of the Fourth International Workshop on Computer Algebra in Scientific Computing, Konstanz, Sept. 22-26, 2001

The book covers various topics of computer algebra methods, algorithms and software applied to scientific computing. An important topic presented in the book, which may be of interest to researchers and engineers, is the application of computer algebra methods to the development of new efficient analytic and numerical solvers, both for ordinary and partial differential equations. A specific feature of the book is an intense use of advanced software systems like Mathematica, Maple etc. for the solution of problems as outlined above and for the industrial application of computer algebra for simulation. The book will be useful for researchers and engineers who apply advanced computer algebra methods for the solution of their problems. Front Matter....Pages I-XI Jets. A Maple -Package for Formal Differential Geometry....Pages 1-12 Computing Stratifications of Quotients of Finite Groups and an Application to Shape Memory Alloys....Pages 13-23 A MuPAD Library for Differential Equations....Pages 25-42 Algebraic Identification Algorithm and Application to Dynamical Systems....Pages 43-61 Cooperation between a Dynamic Geometry Environment and a Computer Algebra System for Geometric Discovery....Pages 63-74 On the Stability of Steady Motions of Solar-Sail Satellite....Pages 75-82 Application of Computer Algebra for Investigation of Group Properties of the Navier-Stokes Equations for Compressible Viscous Heat-Conducting Gas....Pages 83-89 Mathematica and Nilpotent Lie Superalgebras....Pages 91-105 Neighborhoods of an Ordinary Linear Differential Equation....Pages 107-121 Invariants of Finite Groups and Involutive Division....Pages 123-135 Symbolic Computation and Boundary Conditions for the Wave Equation....Pages 137-147 Parametric Systems of Linear Congruences....Pages 149-166 Bifurcation Analysis of Low Resonant Case of the Generalized Henon - Heiles System....Pages 167-175 An Involutive Reduction Method to Find Invariant Solutions for Partial Differential Equations....Pages 177-186 Recurrence Functions and Numerical Characteristics of Graphs....Pages 187-194 A New Combinatorial Algorithm for Large Markov Chains (Extended Abstract)....Pages 195-211 GROOME - Tool Supported Graphical Object Oriented Modelling for Computer Algebra and Scientific Computing....Pages 213-232 Construction of Janet Bases I. Monomial Bases....Pages 233-247 Construction of Janet Bases II. Polynomial Bases....Pages 249-263 Low-Dimensional Quasi-Filiform Lie Algebras with Great Length....Pages 265-282 Algebraic Methods for Sectioning Parametric Surfaces....Pages 283-295 The Methods of Computer Algebra and the Arnold-Moser Theorem....Pages 297-308 Symbolic Algorithms of Algebraic Perturbation Theory: Hydrogen Atom in the Field of Distant Charge....Pages 309-322 Perturbation versus Differentiation Indices....Pages 323-337 Employment of the Gröbner Bases in Analysis of Systems Having Algebraic First Integrals....Pages 339-346 “Coalgebra” Structures on 1-Homological Models for Commutative Differential Graded Algebras....Pages 347-361 Conservative Finite Difference Schemes for Cosymmetric Systems....Pages 363-375 A Mathematica Solver for Two-Point Singularly-Perturbed Boundary Value Problems....Pages 377-390 A New Algorithm for Computing Cohomologies of Lie Superalgebras....Pages 391-398 Parallel Computing with Mathematica....Pages 399-399 Solution of Systems of Linear Diophantine Equations....Pages 401-415 SYMOPT: Symbolic Parametric Mathematical Programming....Pages 417-429 Representing Graph Properties by Polynomial Ideals....Pages 431-444 Parametric G 1 -Blending of Several Surfaces....Pages 445-459 A Method of Logic Deduction and Verification in KBS Using Positive Integers....Pages 461-475 Progressive Long Waves on a Slope (A New Solution to the Euler Equation?)....Pages 477-489 The Method of Newton Polyhedra for Investigating Singular Positions of Some Mechanisms....Pages 491-498 Algebraic Predicates for Empirical Data....Pages 499-512 Fractional Driftless Fokker-Planck Equation with Power Law Diffusion Coefficients....Pages 513-528 Factorization of Overdetermined Systems of Linear Partial Differential Equations with Finite-Dimensional Solution Space....Pages 529-539 Semilinear Motion Planning Among Moving Objects in REDLOG....Pages 541-553 Back Matter....Pages 555-555 CASC 2001 continues a tradition ~ started in 1998 ~ of international con­ ferences on the latest advances in the application of computer algebra systems to the solution of various problems in scientific computing. The three ear­ (CASs) lier conferences in this sequence, CASC'98, CASC'99, and CASC 2000, were held, Petersburg, Russia, in Munich, Germany, and in Samarkand, respectively, in St. Uzbekistan, and proved to be very successful. We have to thank the program committee, listed overleaf, for a tremendous job in soliciting and providing reviews for the submitted papers. There were more than three reviews per submission on average. The result of this job is reflected in the present volume, which contains revised versions of the accepted papers. The collection of papers included in the proceedings covers various topics of computer algebra methods, algorithms and software applied to scientific computing. In particular, five papers are devoted to the implementation of the analysis of involutive systems with the aid of CASso The specific examples include new efficient algorithms for the computation of Janet bases for monomial ideals, involutive division, involutive reduction method, etc. A number of papers deal with application of CASs for obtaining and vali­ dating new exact solutions to initial and boundary value problems for partial differential equations in mathematical physics. Several papers show how CASs can be used to obtain analytic solutions of initial and boundary value problems for ordinary differential equations and for studying their properties.