Numerical Analysis and Its Applications

This book constitutes the refereed proceedings of the First International Workshop on Numerical Analysis and Its Applications, WNAA'96, held in Rousse, Bulgaria, in June 1996.
The 57 revised full papers presented were carefully selected and reviewed for inclusion in the volume; also included are 14 invited presentations. All in all, the book offers a wealth of new results and methods of numerical analysis applicable in computational science, particularly in computational physics and chemistry. The volume reflects that the cooperation of computer scientists, mathematicians and scientists provides new numerical tools for computational scientists and, at the same time, stimulates numerical analysis.

The Newtonian continuation method for numerical study of 3D polaron problem.- CANM in numerical investigation of QCD problems.- Parallel iterative solvers for banded linear systems.- Finite element approximations of some central curves.- Utilization of CANM for magnetic field calculation.- Numerical algorithm for simulation of coupled heat-mass transfer and chemical reaction in two-phase steady flow.- Basic techniques for numerical linear algebra on bulk synchronous parallel computers.- Convergence of a Crank-Nicolson difference scheme for heat equations with interface in the heat flow and concentrated heat capacity.- Treatment of large air pollution models.- Boundary Value Methods for the numerical approximation of ordinary differential equations.- Fast algorithms for problems on thermal tomography.- Convergence in iterative polynomial root-finding.- Splitting time methods and one dimensional special meshes for reaction-diffusion parabolic problems.- High-order stiff ODE solvers via automatic differentiation and rational prediction.- The use of discrete sine transform in computations with Toeplitz matrices.- A finite state stochastic minimax optimal control problem with infinite horizon.- Verified solving of linear systems with uncertainties in Maple.- Iterative Monte Carlo algorithms for linear algebra problems.- Operator problems in strengthened Sobolev spaces and numerical methods for them.- Convex combinations of matrices — Nonsingularity and Schur stability.- Numerical solution of a BVP in hydrodynamics (thermocapillary convection).- Componentwise error bounds and direct linear system solving.- A method for solving the spectral problem for complex matrices.- Interpolation technique and convergence rate estimates for finite difference method.- Least squares and total least squares methods in image restoration.- Conforming spectral domain decomposition schemes.- Newton's method for solution of one complex eigenvalue problem.- Calculation of bifurcation states in the circle Josefsson's conversion.- Numerical methods for computation of the double layer logarithmic potential.- Numerical analysis in singularly perturbed boundary value problems modelling heat transfer processes.- Improved perturbation bounds for the matrix exponential.- Spectral portrait of matrices by block diagonalization.- Explicit difference schemes with variable time steps for solving stiff systems of equations.- Difference schemes for the Darboux problem with functional dependence.- Displacement decomposition circulant preconditioners for almost incompressible 2D elasticity systems.- Numerical solution of differential equations with trigonometric coefficients in mathematical models of electric motors.- Stability of difference schemes with variable weights.- Relative precision in the inductive assertion method.- Third order explicit method for the stiff ordinary differential equations.- Justification of difference schemes for derivative nonlinear evolution equations.- On the growth problem for D-optimal designs.- A Cray T3D performance study.- Using dense matrix computations in the solution of sparse problems.- Integration of some constitutive relations of plain strain elastoplasticity using modified Runge-Kutta methods.- High performance solution of linear systems arising from conforming spectral approximations for non-conforming domain decompositions.- Stabilization and experience with the partitioning method for tridiagonal systems.- Numerical solution of high order matrix Riccati equations.- A variational parameters-to-estimate-free nonlinear solver.- Computation model for internal chemical-reacting flows through curved channels.- Compactly supported fundamental functions for bivariate hermite spline interpolation and triangular finite elements of HCT type.- The effectiveness of band-Toeplitz preconditioners: A survey.- Grid approximations of the solution and diffusion flux for singularly perturbed equations with Neumann boundary conditions.- Bessel and Neumann fitted methods for the numerical solution of the Schrödinger equation.- On the data re-processing-free algorithm in the initial state estimation problem for parabolic systems.- Exploiting the natural partitioning in the numerical solution of ODE systems arising in atmospheric chemistry.- Existence and stability of traveling discrete shocks.- Numerical analysis of density dependence for effective transport kinetic diameter of real fluids.- On a feasible descent algorithm for solving min-max problems.- Rate of convergence of a numerical procedure for impulsive control problems.- Coarse-grain parallelisation of multi-implicit Runge-Kutta methods.- Mosaic ranks and skeletons.- Numerical techniques for solving convection-diffusion problems.- Explicit fifth order Runge-Kutta methods with five stages for quadratic ODEs.- P-stable mono-implicit Runge-Kutta-Nyström modifications of the Numerov method.- The V-Ray technology of optimizing programs to parallel computers.- Applications of Steklov-type eigenvalue problems to convergence of difference schemes for parabolic and hyperbolic equations with dynamical boundary conditions.- Two-step P-stable methods with phase-lag of order infinity for the numerical solution of special second order initial value problems.- Notes on the classification of numerical algorithms with respect to their stability to roundoff errors.- New IMGS-based preconditioners for least squares problems.- Numerical algorithm for studying heat transfer in a glass melting furnace.- Identification of the heat-transfer in a glass melting furnace.