Differential Equations and Numerical Mathematics - 1st Edition - ISBN: 9780080264912, 9781483154541

Differential Equations and Numerical Mathematics

1st Edition

Selected Papers Presented to a National Conference Held in Novosibirsk, September 1978

Editors: G. I. Marchuk
eBook ISBN: 9781483154541
Imprint: Pergamon
Published Date: 1st January 1982
Page Count: 164
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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.

Table of Contents

Section A. Cubature Formulae and Functional Analysis

1. 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 Equations

7. 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 Mathematics

12. 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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About the Editor

G. I. Marchuk

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