Polozhii / Sneddon / Stark The Method of Summary Representation for Numerical Solution of Problems of Mathematical Physics

1. Auflage 2014
ISBN: 978-1-4831-8546-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 79, 304 Seiten, Web PDF

Reihe: International Series in Pure and Applied Mathematics

Pure and Applied Mathematics, Volume 79: The Method of Summary Representation for Numerical Solution of Problems of Mathematical Physics presents the numerical solution of two-dimensional and three-dimensional boundary-value problems of mathematical physics. This book focuses on the second-order and fourth-order linear differential equations. Organized into two chapters, this volume begins with an overview of ordinary finite-difference equations and the general solutions of certain specific finite-difference equations. This text then examines the various methods of successive approximation that are used exclusively for solving finite-difference equations. This book discusses as well the established formula of summary representation for certain finite-difference operators that are associated with partial differential equations of mathematical physics. The final chapter deals with the formula of summary representation to enable the researcher to write the solution of the corresponding systems of linear algebraic equations in a simple form. This book is a valuable resource for mathematicians and physicists.

Autoren/Hrsg.

Polozhii, G. N.

Sneddon, I. N.

Stark, M.

Gravett, K. A. H.

Inhaltsverzeichnis

1;Front Cover;1
2;The Method of Summary Representation for Numerical Solution of Problems of Mathematical Physics;4
3;Copyright Page;5
4;Table of Contents;6
5;Author's Preface to the English Edition;9
6;Preface;10
7;Introduction;12
8;CHAPTER 1. General Theory of the One-dimensional Problem of Eigenvalues and Eigenfunctions
of Discrete Argument. Matrices of Type .;22
8.1;§ 1. Ordinary Finite-difference Equations;22
8.2;§ 2. General Problem of Eigenvalues and Eigenfunctions of Discrete Argument. Matrices of Type .;36
8.3;§ 3. Solution of Particular Boundary-value Problems, and the Construction of Fundamental Matrices in Explicit Form;58
8.4;§ 4. On Special Functions of Discrete Argument,

and Special Matrices of Type .;70
9;CHAPTER 2. Numerical Solution of Two-dimensional and Three-dimensional Boundary-value Problems of Mathematical Physics;88
9.1;§ 1. Solution of Boundary-value Problems for Second-order Elliptic Differential Equations with Constant Coefficients;89
9.2;§ 2. Solution of Boundary-value Problems for Fourth-order Elliptic Differential Equations with Constant Coefficients;135
9.3;§ 3. Formulae of Summary Representation for Finite-difference Equations, corresponding to Second-order Parabolic Differential Equations with Constant Coefficients;162
10;§ 4. Solution of Finite-difference Boundary-value Problems, connected with Boundary-value Problems for Second-order Hyperbolic Differential Equations with Constant Coefficients;179
10.1;Supplement to the English Edition;218
10.2;§ 1. Alternating Iterative Method for the Numerical Solution of Connection Equations;220
10.3;§ 2. On the Approach to the Limit in Certain Formulae of Summary Representation;230
10.4;§ 3. On the Application of this Method of Summary Representation to the Solution of Problems of Filtration under Pressure;235
11;§ 4. On the Solution of Bending and Torsion Problems for Prismatic Beams by the Method of Summary Representation;244
11.1;§ 4.1 Equations of Hyperbolic Type with two Independent Variables;179
11.2;§ 4.2 Hyperbolic Equations with three Independent Variables;185
11.3;References;212
12;§ 5. On the Application of the Method of Summary Representation to Biharmonic Problems of the Bending of Plates;256
13;§ 6. On Certain Formulae of Summary Representation;267
13.1;§ 6.1. Formulae of Summary Representation for Annular Sectors and for Annuli;267
13.2;§ 6.2. Formulae of Summary Representation for Sectors and Circles;278
13.3;§ 6.3. Formulae of Summary Representation for Angles and Planes;283
13.4;§ 6.4. On the Solutions of Boundary-value Problems, and Certain Generalizations;285
14;§ 7. Bibliography of the Scientific Works of Professor G.N.Polozhii;290
15;Index;296
16;OTHER TITLES IN THE SERIES IN PURE AND APPLIED MATHEMATICS;302