Differential Equations and Numerical Mathematics : Selected Papers Presented to a National Conference Held in Novosibirsk, September 1978

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. Content: Some Other Pergamon Titles of Interest, Page ii Front Matter, Page iii Copyright, Page iv Preface, Page v, G.I. MARCHUK CHAPTER 1 - On an analogue of Plancherel's theorem and on the qualitative character of the spectrum of a self-adjoint operator, Pages 3-7, R.A. ALEXANDRJAN, R.Z. MKRTCHJAN CHAPTER 2 - Self-adjoint operators in spaces of functions of an infinite number of variables, Pages 9-17, YU.M. BEREZANSKII CHAPTER 3 - Multidimensional non-linear spectral boundary value problems and soliton superposition of their asymptotic solutions, Pages 19-26, S.JU. DOBROKHOTOV, V.P. MASLOV CHAPTER 4 - Réduction de la dimension dans un problème de contrôle optimal, Pages 27-33, J-L. LIONS CHAPTER 5 - Embedding theorems for a class of weight spaces and applications, Pages 35-38, P.I. LIZORKIN, M. OTELBAEV CHAPTER 6 - Theory of multipliers in spaces of differentiable functions and applications, Pages 39-46, V.G. MAZYA, T.O. SHAPOSHNIKOVA CHAPTER 7 - On the roots of Euler polynomials, Pages 49-68, S.L. SOBOLEV CHAPTER 8 - On certain mathematical problems in hydrodynamics, Pages 69-80, A.A. DEZIN, T.I. ZELENYAK, V.N. MASLENNIKOVA CHAPTER 9 - On the solvability of the Sturm–Liouville inverse problem on the entire line, Pages 81-86, B.M. LEVITAN CHAPTER 10 - Asymptotic properties of solutions of partial differential equations, Pages 87-96, O.A. OLEINIK CHAPTER 11 - Boundary value problems for weakly elliptic systems of differential equations, Pages 97-103, R.S. SAKS CHAPTER 12 - A generalization of the finite element method for solution of hyperbolic equations, Pages 107-111, J. BRILLA CHAPTER 13 - An asymptotic minimization of computational costs for solving strongly elliptic boundary value problems, Pages 113-119, E.G. DJAKONOV CHAPTER 14 - On optimal algorithms for solving the problems of numerical mathematics, Pages 121-125, V.V. IVANOV CHAPTER 15 - Game theory and optimality of iterative methods, Pages 127-132, V.I. LEBEDEV CHAPTER 16 - The block-relaxation method for solution of the Dirichlet problem, Pages 133-138, YU.A. KUZNETSOV CHAPTER 17 - On the asymptotic behaviour of solutions of the homogeneous transport equation, Pages 139-143, I. MAREK CHAPTER 18 - The method of inner boundary conditions and its applications. A new approach to the numerical solution of boundary integral equations, Pages 145-150, V.S. RJABENKIJ CHAPTER 19 - Inverse problems and energy inequalities, Pages 151-156, V.G. ROMANOV