Proceedings of the Conference on Applied Mathematics and Scientific Computing, 2005

This book brings together contributed papers presenting new results covering different areas of applied mathematics and scientific computing. Firstly, four invited lectures give state-of-the-art presentations in the fields of numerical linear algebra, shape preserving approximation and singular perturbation theory. Then an overview of numerical solutions to skew-Hamiltonian and Hamiltonian eigenvalue problems in system and control theory is given by Benner, Kressner and Mehrmann. The important issue of structure preserving algorithms and structured condition numbers is discussed. Costantini and Sampoli review the basic ideas of the abstract schemes and show that they can be used to solve any problem concerning the construction of spline curves subject to local constraints. Kvasov presents a novel approach in solving the problem of shape preserving spline interpolation. Formulating this problem as a differential multipoint boundary value problem for hyperbolic and biharmonic tension splines he considers its finite difference approximation. Miller and Shishkin consider the Black-Scholes equation that, for some values of the parameters, may be a singularly perturbed problem. They construct a new numerical method, on an appropriately fitted piecewise-uniform mesh, which is parameter-uniformly convergent.

Invited Lectures.- Skew-Hamiltonian and Hamiltonian Eigenvalue Problems: Theory, Algorithms and Applications.- A General Frame for the Construction of Constrained Curves.- DMBVP for Tension Splines.- Robust Numerical Methods for the Singularly Perturbed Black-Scholes Equation.- Contributed Lectures.- On Certain Properties of Spaces of Locally Sobolev Functions.- On Some Properties of Homogenised Coefficients for Stationary Diffusion Problem.- Solving Parabolic Singularly Perturbed Problems by Collocation Using Tension Splines.- On Accuracy Properties of One-Sided Bidiagonalization Algorithm and Its Applications.- Knot Insertion Algorithms for Weighted Splines.- Numerical Procedures for the Determination of an Unknown Source Parameter in a Parabolic Equation.- Balanced Central NT Schemes for the Shallow Water Equations.- Hidden Markov Models and Multiple Alignments of Protein Sequences.- On Strong Consistency for One-Step Approximations of Stochastic Ordinary Differential Equations.- On the Dimension of Bivariate Spline Space S31(?).- Total Least Squares Problem for the Hubbert Function.- Heating of Oil Well by Hot Water Circulation.- Geometric Interpolation of Data in $$\mathbb{R}$$ 3.- One-Dimensional Flow of a Compressible Viscous Micropolar Fluid: Stabilization of the Solution.- On Parameter Classes of Solutions for System of Quasilinear Differential Equations.- Algebraic Proof of the B-Spline Derivative Formula.- Relative Perturbations, Rank Stability and Zero Patterns of Matrices.- Numerical Simulations of Water Wave Propagation and Flooding.- Derivation of a Model of Leaf Springs.- Quantum Site Percolation on Amenable Graphs.- Order of Accuracy of Extended Weno Schemes.