Computers & Mathematics with Applications

article

Iterative Domain Decomposition Algorithms for the Solution of 2-D Eddy Current Problem

I. P. Boglaev, V. V. Sirotkin

Computers and Mathematics with Applications > 1995 > 29 > 1 > 67-81

Iterative domain decomposition algorithms are applied to the solution of two-dimensional eddy current problem. The system of differential equations describing this problem is considered as singularly perturbed problem. Convergence of these algorithms is established. Several numerical experiments are presented.

article

Shock Capturing for Supercritical, Free-Surface Flows in Curvilinear Channel Geometries

P. Glaister

Computers and Mathematics with Applications > 1995 > 29 > 1 > 27-37

A shock-capturing scheme is developed for the shallow water equations governing steady, supercritical flow in two dimensions in channels with a curvilinear coordinate geometry. The scheme incorporates a special averaging procedure of the flow variables as well as details of the transformation that maps a nonrectangular physical domain for a general channel transition.

article

Polynomial Zerofinding Iterative Matrix Algorithms

F. Malek, R. Vaillancourt

Computers and Mathematics with Applications > 1995 > 29 > 1 > 1-13

Newbery's method is completed to a method for the construction of a (complex) symmetric or nonsymmetric matrix with a given characteristic polynomial. The methods of Fiedler, Schmeisser, and Dorfler and Schmeisser for similar constructions of symmetric matrices are reviewed. Polynomials found in the literature are solved iteratively by one of Fiedler's methods with initial values supplied either...

article

Exact Solutions to KdV Equations with Variable Coefficients and/or Nonuniformities

M. Vlieg-Hulstman, W. D. Halford

Computers and Mathematics with Applications > 1995 > 29 > 1 > 39-47

A class of KdV equations with variable coefficients and/or nonuniformities is discussed. We derive easily the constraint conditions which must apply to this class in order to obtain exact solutions. By a direct method, we obtain solutions in a number of generic as well as specific cases.

article

Description of Complex and Sharp Interface with Fixed Grids in Incompressible and Compressible Fluid

T. Yabe, F. Xiao

Computers and Mathematics with Applications > 1995 > 29 > 1 > 15-25

A method to treat a sharp discontinuity by the density function is proposed. The surface of the density function is described by one grid throughout the calculation even when the surface is largely distorted. This description is made possible by the CIP method combined with variable transformation. This scheme can be used for detecting sharp boundary of compressible fluid as well as incompressible...

article

An Efficient Shock Capturing Scheme for Two-Dimensional, Open Channel, Unsteady Flows in a Generalised Coordinate System

P. Glaister

Computers and Mathematics with Applications > 1995 > 29 > 1 > 83-88

An efficient algorithm based on flux difference splitting is presented for the solution of two-dimensional, open channel flows. A transformation maps a nonrectangular, physical domain into a rectangular one. The governing equations are then the shallow water equations, including terms of slope and friction, in a generalised coordinate system. A regular mesh on a rectangular computational domain...

article

A Parallel Solver for Circulant Block-Tridiagonal Systems

K.-L. Chung, Y.-H. Tsai, W.-M. Yan

Computers and Mathematics with Applications > 1995 > 29 > 1 > 109-113

Generalizing Muller and Scheerer's method which is used to parallelize the tridiagonal solvers, this paper presents a parallel method for solving the circulant block-tridiagonal systems. The applications of our result to solve the block-tridiagonal systems, the banded systems, and the circulant tridiagonal systems (for example, solving the closed B-spline curve fitting) are also addressed.

article

Decay of Solutions of the Wave Equation Outside Rough Surfaces

B. Ducomet

Computers and Mathematics with Applications > 1995 > 29 > 1 > 89-108

In the first part of this paper, we prove the decay of local energy for the solutions of the wave equation in an exterior domain outside a two-dimensional rough surface in R ³ which satisfies an additional geometric condition, weak star-shaped condition WSS, implying the absence of trapped rays. Moreover, if the stronger star-shaped condition SS of Morawetz is added, the rate of decay...

article

An Artificial Intelligence Approach for the Generation and Enumeration of Perfect Matchings on Graphs

M. M. Balakrishnarajan, P. Venuvanalingam

Computers and Mathematics with Applications > 1995 > 29 > 1 > 115-121

A new search based algorithm is developed for an effective combinatorial exploration of all the perfect matchings on a general graph. The algorithm makes use of a relations based representation of the graph and is completely independent of the nature of the graph. Though this is a typical NP-class subgraph enumeration problem, the search ranks high in selectivity without compromising accuracy using...

article

A Petrov-Galerkin Spectral Element Technique for Heterogeneous Porous Media Flow

K. Black

Computers and Mathematics with Applications > 1995 > 29 > 1 > 49-65

A novel spectral element technique is examined in which the test functions are different from the approximating elements. Examples are given for a simple 1-D Helmholtz equation, Burger's Equation with a small viscosity, and for Darcy's Equation with a discontinuous hydraulic conductivity.

article

The Computer Searches for Pascal Conics

S. C. Chou, X. S. Gao

Computers and Mathematics with Applications > 1995 > 29 > 2 > 63-71

An approach to discovering new theorems in geometry using numerical examples is discussed. Four classes of theorems related to Pascal conics have been discovered by this approach. Two of them are new.

article

Towards Automating Duality

C. Brink, D. M. Gabbay, H. J. Ohlbach

Computers and Mathematics with Applications > 1995 > 29 > 2 > 73-90

Dualities between different theories occur frequently in mathematics and logic--between syntax and semantics of a logic, between structures and power structures, between relations and relational algebras, to name just a few. In this paper, we show for the case of structures and power structures how corresponding properties of the two related structures can be computed fully automatically by means...

article

The Shortest Single Axioms for Groups of Exponent 4

K. Kunen

Computers and Mathematics with Applications > 1995 > 29 > 2 > 1-12

We study equations of the form (α = χ), which are single axioms for groups of exponent 4, where α is a term in product only. Every such α must have at least nine variable occurrences, and there are exactly three such α of this size, up to variable renaming and mirroring. These terms were found by an exhaustive search through all terms of this form. Automated techniques were used in two ways: to...

article

The Boyer-Moore Theorem Prover and Its Interactive Enhancement

R. S. Boyer, M. Kaufmann, J. S. Moore

Computers and Mathematics with Applications > 1995 > 29 > 2 > 27-62

The so-called Boyer-Moore Theorem Prover (otherwise known as Nqthm) has been used to perform a variety of verification tasks for two decades. We give an overview of both this system and an interactive enhancement of it, Pc-Nqthm, from a number of perspectives. First, we introduce the logic in which theorems are proved. Then, we briefly describe the two mechanized theorem proving systems. Next,...

article

An Overview of Rewrite Rule Laboratory (RRL)

D. Kapur, H. Zhang

Computers and Mathematics with Applications > 1995 > 29 > 2 > 91-114

RRL (Rewrite Rule Laboratory) was originally developed as an environment for experimenting with automated reasoning algorithms for equational logic based on rewrite techniques. It has now matured into a full-fledged theorem prover which has been used to solve hard and challenging mathematical problems in automated reasoning literature as well as a research tool for investigating the use of formal...

article

The Resonance Strategy

L. Wos

Computers and Mathematics with Applications > 1995 > 29 > 2 > 133-178

Especially in mathematics and in logic, lemmas (basic truths) play a key role for proving theorems. In ring theory, for example, a useful lemma asserts that, for all elements x, the product in either order of 0 and x is 0; in two-valued sentential (or propositional) calculus, a useful lemma asserts that, for all x, x implies x. Even in algorithm writing and in circuit design, lemmas play a key role:...

article

Automated Reasoning about Cubic Curves

R. Padmanabhan, W. McCune

Computers and Mathematics with Applications > 1995 > 29 > 2 > 17-26

It is well known that the n-ary morphisms defined on projective algebraic curves satisfy some strong local-to-global equational rules of derivation not satisfied in general by universal algebras. For example, every rationally defined group law on a cubic curve must be commutative. Here, we extract from the geometry of curves a first-order property (gL) satisfied by all morphisms defined on these...

article

Automated Reasoning and Exhaustive Search: Quasigroup Existence Problems

J. Slaney, M. Fujita, M. Stickel

Computers and Mathematics with Applications > 1995 > 29 > 2 > 115-132

This is a report of research carried out during 1992 and 1993 in which three different automated reasoning programs--DDPP, FINDER, and MGTP--were applied to a series of exhaustive search problems in the theory of quasigroups. All three of the programs succeeded in solving previously open problems concerning the existence of quasigroups satisfying certain additional conditions. Using different programs...

article

Single Identities for Ternary Boolean Algebras

R. Padmanabhan, W. McCune

Computers and Mathematics with Applications > 1995 > 29 > 2 > 13-16

We present the first known single axioms for ternary Boolean algebra. The first single axiom was found algebraically by a previous technique of Padmanabhan and Quackenbush; then simpler single axioms were found by using the automated reasoning program Otter.

article

A New Decomposition Method for Stochastic Dynamic Stabilization

P. Florchinger

Computers and Mathematics with Applications > 1995 > 29 > 3 > 31-36

The aim of this paper is to prove that the stabilizability of a controlled nonlinear stochastic system can be deduced from the stabilizability of a [ldquo ]reduced[rdquo ] system for which the existence of a stabilizing feedback law can be decided more easily. This result extends the well-known deterministic [ldquo ]chain of integrator lemma[rdquo ] by using a different scheme of reduction for the...

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Computers & Mathematics with Applications

Iterative Domain Decomposition Algorithms for the Solution of 2-D Eddy Current Problem

Shock Capturing for Supercritical, Free-Surface Flows in Curvilinear Channel Geometries

Polynomial Zerofinding Iterative Matrix Algorithms

Exact Solutions to KdV Equations with Variable Coefficients and/or Nonuniformities

Description of Complex and Sharp Interface with Fixed Grids in Incompressible and Compressible Fluid

An Efficient Shock Capturing Scheme for Two-Dimensional, Open Channel, Unsteady Flows in a Generalised Coordinate System

A Parallel Solver for Circulant Block-Tridiagonal Systems

Decay of Solutions of the Wave Equation Outside Rough Surfaces

An Artificial Intelligence Approach for the Generation and Enumeration of Perfect Matchings on Graphs

A Petrov-Galerkin Spectral Element Technique for Heterogeneous Porous Media Flow

The Computer Searches for Pascal Conics

Towards Automating Duality

The Shortest Single Axioms for Groups of Exponent 4

The Boyer-Moore Theorem Prover and Its Interactive Enhancement

An Overview of Rewrite Rule Laboratory (RRL)

The Resonance Strategy

Automated Reasoning about Cubic Curves

Automated Reasoning and Exhaustive Search: Quasigroup Existence Problems

Single Identities for Ternary Boolean Algebras

A New Decomposition Method for Stochastic Dynamic Stabilization

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