Differential equations and numerical mathematics : selected papers presented to a national conference held in Novosibirsk, September 1978 / edited by G. I. Marchuk.

Format:

Book

Contributor:

Marchuk, G. I. (Guriĭ Ivanovich), 1925- editor.

Language:

English

Subjects (All):

Differential equations.

Numerical analysis.

Functional analysis.

Physical Description:

1 online resource (165 p.)

Edition:

First English edition.

Place of Publication:

Oxford, England : Pergamon Press, 1982.

Language Note:

English

Summary:

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

Contents:

Front Cover; Differential Equations and Numerical Mathematics; Copyright Page; Preface; Table of Contents; SECTION A: Cubature Formulae and Functional Analysis; CHAPTER 1. On an analogue of Plancherel's theorem and on the qualitative character of the spectrum of a self-adjoint operator; References; References; CHAPTER 2. Self-adjoint operators in spaces of functions of an infinite number of variables; CHAPTER 3. Multidimensional non-linear spectral boundary value problems and soliton superposition of their asymptotic solutions; 1. A non-linear spectral boundary value problem of Steklov type

2. Asymptotic complex-valued solutions, concentrated in the neighbourhood of closed geodesies3. ""Non-linear superposition"" of asymptotic solutions, multidimensional Dirichlet series and real-valued asymptotic solutions; 4. Example; 5. Problem of reflection from a boundary and finite-gap almost periodic solutions; References; CHAPTER 4. Réduction de la dimension dans un probléme de contrôle optimal; Introduction; 1. Position du probléme; 2. Enonce du résultat; 3. Bornes supérieures; 4. Dualité; 5. Bornes inférieures; Références

2. The second asymptotic formula3. The domain of validity of formula II; 4. The magnitude of qlIj{k) and the error for large values of q; 5. The first asymptotic formula; 6. Estimation of ζ; 7. The estimation of Σ1; 8. The estimation of Σ2; 9. The estimation of the error of formula I; 10. The estimation of the length of productive intervals for q = 0(k-1/2); References; CHAPTER 8. On certain mathematical problems in hydrodynamics; 1. On the approximation of solenoidal vector fields

2. The second problem we should like to consider is the investigation of the decay and rise of vorticity in a moving continuous mediumReferences; CHAPTER 9. On the solvability of the Sturm-Liouville inverse problem on the entire line; 1. Solution of the inverse problem on the entire line by a spectral matrix function; 2. Application to the Korteveg-de Vries equation; References; CHAPTER 10. Asymptotic properties of solutions of partial differential equations; References; CHAPTER 11. Boundary value problems for weakly elliptic systems of differential equations; References

SECTION C: Numerical Mathematics

Notes:

Description based upon print version of record.

Includes bibliographical references at the end of each chapters.

Description based on print version record.

ISBN:

1-4831-5454-8