| Description |
1 online resource (448 pages) |
| Series |
De Gruyter studies in mathematics, 0179-0986 ; 42 |
|
De Gruyter studies in mathematics ; 42. 0179-0986
|
| Contents |
Preface; 0 Introduction; 1 Green's Functions for ODE; 1.1 Standard Procedure for Construction; 1.2 Symmetry of Green's Functions; 1.3 Alternative Construction Procedure; 1.4 Chapter Exercises; 2 The Laplace Equation; 2.1 Method of Images; 2.2 Conformal Mapping; 2.3 Method of Eigenfunction Expansion; 2.4 Three-Dimensional Problems; 2.5 Chapter Exercises; 3. The Static Klein-Gordon Equation; 3.1 Definition of Green's Function; 3.2 Method of Images; 3.3 Method of Eigenfunction Expansion; 3.4 Three-Dimensional Problems; 3.5 Chapter Exercises; 4 Higher Order Equations |
|
4.1 Definition of Green's Function4.2 Rectangular-Shaped Regions; 4.3 Circular-Shaped Regions; 4.4 The equation?2?2w(P) +?4w(P) = 0; 4.5 Elliptic Systems; 4.6 Chapter Exercises; 5 Multi-Point-Posed Problems; 5.1 Matrix of Green's Type; 5.2 Influence Function of a Multi-Span Beam; 5.3 Further Extension of the Formalism; 5.4 Chapter Exercises; 6 PDE Matrices of Green's type; 6.1 Introductory Comments; 6.2 Construction of Matrices of Green's Type; 6.3 Fields of Potential on Surfaces of Revolution; 6.4 Chapter Exercises; 7 Diffusion Equation; 7.1 Basics of the Laplace Transform |
|
7.2 Green's Functions7.3 Matrices of Green's Type; 7.4 Chapter Exercises; 8 Black-Scholes Equation; 8.1 The Fundamental Solution; 8.2 Other Green's Functions; 8.3 A Methodologically Valuable Example; 8.4 Numerical Implementations; 8.5 Chapter Exercises; Appendix Answers to Chapter Exercises; Bibliography; Index |
| Summary |
This monograph is looking at applied elliptic and parabolic type partial differential equations in two variables. The elliptic type includes the Laplace, static Klein-Gordon and biharmonic equation. The parabolic type is represented by the classical heat equation and the Black-Scholes equation which has emerged as a mathematical model in financial mathematics. This book is a useful source for everyone who is studying or working in the fields of science, finance, or engineering that involve practical solution of partial differential equations |
| Analysis |
Elliptic |
|
Green's Function |
|
Parabolic |
|
Partial Differential Equation |
| Bibliography |
Includes bibliographical references and index |
| Notes |
In English |
|
Print version record |
| Subject |
Green's functions.
|
|
MATHEMATICS -- Differential Equations -- Partial.
|
|
Green's functions
|
|
Green-Funktion
|
| Form |
Electronic book
|
| Author |
Melnikov, Max Y
|
| LC no. |
2011032101 |
| ISBN |
9783110253399 |
|
3110253399 |
|
311025302X |
|
9783110253023 |
|
9781280597640 |
|
128059764X |
|
9786613627476 |
|
661362747X |
|
