D. Bainov Knihy

This work explores various advanced topics in mathematical analysis and differential equations. It addresses the inverse scattering problem for the wave equation with discontinuous wave speeds and presents difference methods for impulsive partial differential equations. The text examines radially symmetric solutions of semilinear elliptic equations and introduces weighted Poincaré-type inequalities in multiple dimensions. It discusses matrix nonstationary semigroups and critical points theory, applying these concepts to nonlinear wave equations. The existence of decreasing positive solutions for linear differential equations with delays is investigated, alongside equations in nonlinear membrane theory. Additional topics include the dynamics of clustering neural networks, elliptic equations with measure data, and a novel b-spline finite element method for the advection-diffusion equation. The work delves into coupled elliptic systems relevant to fuel cell modeling and compares deficiency indices of differential expressions. It covers reproducing kernels, inverse formulas for Laplace transforms, and Hankel transforms related to dust diffusion. Asymptotic volume nullification of singular diffusions is analyzed, as well as conditions for the absence of positive solutions in differential inequalities with distributed delays. The stability of large-scale impulsive systems and heat conduction in mediums with thin shells are also dis

Frontmatter -- Contents -- Preface -- Orthogonal polynomials associated with a non-standard measure -- The numerical treatment of ordinary and partial Volterra integro-differential equations -- Numerical methods for y" = f(x, y) -- Numerical-analytical method for finding periodic solutions of nonlinear impulsive singularly perturbed differential systems -- Special algorithms for the numerical integration of problems in orbital dynamics -- Polynomial approximation with side conditions: Recent results and open problems -- Continuous numerical solutions and error bounds for matrix differential equations -- Convergence rate estimates for the finite difference schemes compatible with the smoothness of data -- Numerical solutions of differential-function problems -- An Iterated Method Of Computing The Inverse Mapping -- On using high orders finite elements for solving structural mechanics problems -- Numerical solution of differential equations for the analytic singular value decomposition -- A new trust region algorithm for nonlinear optimization

This collection covers a wide array of advanced mathematical topics and methodologies. It begins with periodic solutions for multi-phase Stefan problems featuring dynamic boundary conditions, followed by discussions on overdetermined problems for elliptic equations. The text explores mixed finite-element methods applicable to flow in porous media and examines limit sets of impulsive dynamical systems. Non-classical dynamic programming in optimal control is addressed, alongside Painleve analysis of nonlinear reaction-diffusion systems. The work delves into weighted interpolation and Hardy inequalities, presenting spectral theoretic applications. It also discusses probabilistic approaches to relativity and gravitation, monodromic unbounded polycycles, and uniform schemes for singularly perturbed scalar initial value problems. Recent developments in the operator theoretical treatment of partial differential equations are highlighted, including the Hilbert-Arnold problem for cubic Hamiltonians and limit cycles. Further topics include periodic solutions of neutral impulsive systems with small delays, analytic-numerical solutions of variable coefficient second-order delay differential equations, and localization of global existence for holomorphic solutions of differential equations with complex parameters. The text also addresses boundary value problems, estimates for solutions of elliptic-parabolic difference differential equati

Frontmatter -- CONTENTS -- Preface -- SPLINES ON S2 FOR SMALL LATITUDES -- The Algebraic Multilevel Iteration Methods - theory and applications -- THE ALGEBRAIC ANALYSIS OF INCOMPLETE FACTORIZATION PRECONDITIONINGS -- Numerical Computation of Incompressible Flows -- Some applications of the Euclidean algorithm -- Best Approximation in Reproducing Kernel Hilbert Spaces -- Chebyshev Spectral Solution of the Burgers Equation with High Wavenumbers -- PADÉ APPROXIMATION AND NUMERICAL INVERSION OF THE LAPLACE TRANSFORM -- On a class of singularly perturbed boundary value problems for which an adaptive mesh technique is necessary -- Some Robust Methods for Nonlinear Parameter Estimation -- INTERPOLATION OF FUNCTION SPACES AND THE CONVERGENCE RATE ESTIMATES FOR THE FINITE DIFFERENCE SCHEMES -- Real Zeros of Holomorphic Functions with Parameters -- Optimal Partitioning in Univariate and Multivariate Approximation -- Asymptotic Behavior of Blow-Up Solutions of the Nonlinear Schrodinger Equation with Critical Power Nonlinearity -- Approximation by Univariate and Bivariate Splines -- Parallelizable PCG Methods for the Cray Y-MP and the TMC CM-2 -- Stability of Finite Difference Formulas for Linear Parabolic Equations -- NONLINEAR SPLINES IN CONVEX AND S-CONVEX INTERPOLATION -- A FAMILY OF FOUR-STEP EXPONENTIAL FITTED PREDICTOR-CORRECTOR METHODS FOR THE NUMERICAL INTEGRATION OF THE SCHRODINGER EQUATION

This book covers a range of advanced topics in numerical methods and mathematical analysis. It begins with methods for solving first-order partial differential equations with impulses and progresses to numerical solutions for singular nonlinear boundary value problems. The text includes a survey on continuous selections for metric projections and explores solutions to specific linear problems and algebraic polynomial operators. Advanced techniques for initial value problems are discussed, along with the construction of 3-D meshes using Delaunay triangulation. The book examines the convergence of finite volume schemes for nonlinear hyperbolic equations and provides an overview of QR methods for large least squares problems involving Kronecker products. It presents a conservative B-spline finite element method for the nonlinear Schrödinger equation and discusses global smoothness preservation through Bernstein polynomial blossoms. Additional topics include a four-point finite volume scheme for diffusion-convection problems, monotone iterations for nonlinear convection-diffusion equations, and an approach to automatic finite element mesh generation. The text also addresses numerical aspects of multivariate interpolation, S-convexity preserving interpolation using rational C1 splines, and essentially non-oscillatory methods for conservation laws. It includes algorithms for floating-point sums without round-off errors, multi-peak