Computational and Applied Mathematics: No. 2 Selected and Revised Papers from the IMACS 13th World Congress, Dublin, Ireland, July 1991

Differential equations are the pre-eminent modelling device of engineering and the applied sciences. This volume contains a refereed subset of papers presented at the 1991 IMACS World Congress. A natural subdivision occurred - General Theory, Specific Differential Equations and Computational Methods. There are eleven papers in the area termed General Theory. Seventeen papers concern Specific Differential Equations - both ordinary and partial - which have been used to model various phenomena. Finally, fourteen papers are devoted to a variety of Computational Methods.

Table of Contents:
General Theory. Asymptotic Derivation of an Evolution Thermoelastic Model for Linear Rods. Physics-like Mathematics in 4D-Implications for Classical and Quantum Mechanics. Walsh Function Analysis of Bilinear Implicit Systems with Split Boundary Conditions. Algebraic Aspects of 2D Singular Systems. Solutions to Lyapunov Stability Problems: Nonlinear Systems with Differentiable Motions. Nonlinear Matrix Differential Equations. A New Framework for Systems Analysis via Geometrical Entropy on Path Space. Algebraic Construction of Integrable Equations in (1+1) and (2+1) Dimensions. Trends in the Methods of Vector Lyapunov Functions. Asymptotic, Homogenization and Galerkin Methods in 3D Beam Theory. Stiff Systems of Second-Order Ordinary Differential Equations. Specific Differential Equations. Semi-symmetry Reduction of PDEs. Group Properties of a Monge-Ampere Type Equation. Least Squares Completions of Nonlinear Higher Index Hessenberg DAEs. An Asymptotic Model for a Detonation in Ducts. Hamiltons's Principle and the Equations of Motion of an Elastic Shell with and without Fluid Loading. Approximate Asymptotic Symmetries. Similarity Analysis for Moving Boundary Parabolic Problems. A Mathematical Problem of Rotary Kiln Reactors. A Uniform Scheme for Certain Riccati-Type Equations. Analysis of an Equation Arising in General Relativity. Bounds for the Solution of a System of Parabolic Equations Arising in Circuit Theory. Symmetry Reduction of a PDE Describing Nonlinear Waves in a Compacting Medium. Piecewise-Linear Approximation of Solutions of Delay-Differential Systems by Walsh Functions. Orthogonal with Non-integrable Weight Function Jacobi Polynomials and Their Application to Singular Integral Equations in Elasticity and Heat Conduction Problems. Invariant Manifold Theorems for the Navier Stokes Equations. Nonlinear Evolution Equations and Painleve Test. On the Analysis of Superharmonic Oscillations. Computational Methods. Asymptotic Behaviour of Coupled Matrix-Riccati-Differential Equation: A Computer Algebra Approach. A Widely Convergent Method (CHM) for the Inverse Problem of Operator Identification. Domain Decomposition Technique for Singularly Perturbed Problems and its Parallel Implementation. The Implicit Euler Method and Singular Perturbation Theory. On the Numerical Stability of Volterra Integro-differential and Integral Equations. Symbolic Computation of Solitons with Macsyma. Overlapping Domain Decomposition Methods for the Simplified Dirichlet-Signorini Problem. Numerical Treatment of Stochastic Volterra Integro-differential Equations. On a Fixed Domain Approach for a Shape Optimization Problem. Application of Renormalisation Group to Turbulence Simulations Using Conditional Averaging. 3D Time Harmonic Acoustic and Electromagnetic Inverse Scattering in the Resonance Region. Interactive REDUCE Programs for Calculating Classical, Non-Classical and Approximate Symmetries of Differential Equations.