Computer Algebra in Scientific Computing Casc'99: Proceedings of the Second Workshop on Computer Algebra in Scientific Computing, Munich, May 31 - Jun

ISBN-13: 9783642643095 / Angielski / Miękka / 2011 / 511 str.

Victor G. Ganzha; Ernst W. Mayr; Evgenii V. Vorozhtsov

Opis

The development of powerful computer algebra systems has considerably ex tended the scope of problems of scientific computing which can now be solved successfully with the aid of computers. However, as the field of applications of computer algebra in scientific computing becomes broader and more complex, there is a danger of separation between theory, systems, and applications. For this reason, we felt the need to bring together the researchers who now ap ply the tools of computer algebra for the solution of problems in scientific computing, in order to foster new and closer interactions. CASC'99 is the second conference devoted to applications of computer al gebra in scientific computing. The first conference in this sequence, CASC'98, was held 20-24 April 1998 in St. Petersburg, Russia. This volume contains revised versions of the papers submitted by the par ticipants and accepted by the program committee after a thorough reviewing process. The collection of papers included in the proceedings covers various topics of computer algebra methods, algorithms and software applied to scien tific computing: symbolic-numeric analysis and solving differential equations, efficient computations with polynomials, groups, matrices and other related objects, special purpose programming environments, application to physics, mechanics, optics and to other areas. In particular, a significant group of papers deals with applications of com puter algebra methods for the solution of current problems in group theory, which mostly arise in mathematical physics."

Spis treści

Solution of Ordinary Differential Equations with MathLie.- Analysis of Stability of Rational Approximations through Computer Algebra.- An Automatic Symbolic-Numeric Taylor Series ODE Solver.- About Normal Form Method.- Computer Algebra Investigation of Equivalence in 4-node Plane Stress/Strain Finite Elements.- Symmetry Theorems for the Newtonian 4- and 5-body Problems with Equal Masses.- Symbolic Derivation of Different Class of High-order Compact Schemes for Partial Differential Equations.- Implementation of Aerodynamic Computations with Mathematica.- Completion of Linear Differential Systems to Involution.- Constrained Hamiltonian Systems and Gröbner Bases.- Construction of Involutive Monomial Sets for Different Involutive Divisions.- Partial Inverse Heuristic for the Approximate Solution of Non-linear Equations.- Computing Cocycles on Simplicial Complexes.- Bifurcations of Maps in the Software Package CONTENT.- Extending a Java Based Framework for Scientific Software-Components.- Symbolic-numeric Investigations for Stability Analysis of Satellite Systems.- Quantization by Presentation: The Nambu-Goto String in 1+3 Dimensions.- One Algorithm of Finding Solutions for the Systems with First Integrals.- Cohomology of Lie Superalgebras of Hamiltonian Vector Fields: Computer Analysis.- Computer Algebra Tools in Construction of Renormgroup Symmetries 251.- Where Numerics Can Benefit from Computer Algebra in Finite Difference Modelling of Fluid Flows.- Effectively Computation of Some Radicals of Submodules of Free Modules.- Computations on Character Tables of Association Schemes.- Investigation of Subgroup Embeddings by the Computer Algebra Package GAP.- An Investigation into Stability of Conservative Mechanical Systems Using Analytic Calculations.- Superfast Computations with Singular Structured Matrices over Abstract Fields.- From Modeling to Simulation with Symbolic Computation: An Application to Design and Performance Analysis of Complex Optical Devices.- A Symbolic Numeric Environment for Analyzing Measurement Data in Multi-Model Settings (Extended Abstract).- Geometric Interpretation of Strong Inconsistency in Knowledge Based Systems.- Indices and Solvability for General Systems of Differential Equations.- Decomposing Systems of Polynomial Equations.- Polynomials with Coefficients of Limited Accuracy.- Localization of Roots of a Polynomial not Represented in Canonical Form.- On Normalization of a Class of Polynomial Hamiltonians: From Ordinary and Inverse Points of View.- On Multivariate Polynomial Decomposition.- Complexity of Monomial Evaluations and Duality.- On the Simplification of Nonlinear DAE Systems in Analog Circuit Design.- Symbolic Analysis of Computational Algorithms with SYDNA.

O autorze

Prof. Dr. Victor Ganzha lehrt am Fachbereich Mathematik/Informatik der Universität-GH Kassel. Er beschäftigt sich mit symbolisch-numerischen Methoden.