Differential Equations and Numerical Mathematics contains selected papers presented in a national conference held in Novosibirsk on September 1978. This book, as the conference, is organized into three sections. Section A describes the modern theory of efficient cubature formulas; embedding theorems; and problems of spectral analysis. Section B considers the theoretical questions of partial differential equations, with emphasis on hyperbolic equations and systems, formulations, and methods for nonclassical problems of mathematical physics. Section C addresses the various problems of numerical mathematics, with focus on the optimum and asymptotically optimum algorithms for solving the problems of numerical mathematics.
Section A. Cubature Formulae and Functional Analysis1. On an Analogue of Plancherel's Theorem and on the Qualitative Character of the Spectrum of a Self-adjoint Operator 2. Self-adjoint Operators in Spaces of Functions of an Infinite Number of Variables 3. Multidimensional Non-linear Spectral Boundary Value Problems and Soliton Superposition of Their Asymptotic Solutions 4. Réduction de la dimension dans un problème de contrôle optimal 5. Embedding Theorems for a Class of Weight Spaces and Applications 6. Theory of Multipliers in Spaces of Differentiable Functions and Applications
Section B. Differential Equations7. On the Roots of Euler Polynomials 8. On Certain Mathematical Problems in Hydrodynamics 9. On the Solvability of the Sturm-Liouville Inverse Problem on the Entire Line 10. Asymptotic Properties of Solutions of Partial Differential Equations 11. Boundary Value Problems for Weakly Elliptic Systems of Differential Equations
Section C. Numerical Mathematics12. A Generalization of the Finite Element Method for Solution of Hyperbolic Equations 13. An Asymptotic Minimization of Computational Costs for Solving Strongly Elliptic Boundary Value Problems 14. On Optimal Algorithms for Solving the Problems of Numerical Mathematics 15. Game Theory and Optimality of Iterative Methods 16. The Block-relaxation Method for Solution of the Dirichlet Problem 17. On the Asymptotic Behavior of Solutions of the Homogeneous Transport Equation 18. The Method of Inner Boundary Conditions and Its Applications. A New Approach to the Numerical Solution of Boundary Integral Equations 19. Inverse Problems and Energy Inequalities
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- © Pergamon 1982
- 1st January 1982
- eBook ISBN: