Green's Functions : Construction and Applications
- Author
- Melnikov, Yu. A.
- Published
- Berlin : De Gruyter, 2012.
- Physical Description
- 1 online resource (448 pages).
- Additional Creators
- Melnikov, Max Y.
Access Online
- Series
- Language Note
- In English.
- 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., and 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 Function -- 4.2 Rectangular-Shaped Regions -- 4.3 Circular-Shaped Regions -- 4.4 The equation ∇2∇2w(P) + λ4w(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 Functions -- 7.3 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.
- Subject(s)
- Other Subject(s)
- ISBN
- 9783110253399 (electronic bk.)
3110253399 (electronic bk.)
311025302X
9783110253023
9781280597640
128059764X
9786613627476
661362747X - Bibliography Note
- Includes bibliographical references and index.
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