Melnikov Green's Functions

Construction and Applications
1. Auflage 2012
ISBN: 978-3-11-025339-9
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, Band 42, 447 Seiten

Reihe: De Gruyter Studies in MathematicsISSN

Green's functions represent one of the classical and widely used issues in the area of differential equations.

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. The book is attractive for practical needs: It contains many easily computable or computer friendly representations of Green's functions, includes all the standard Green's functions and many novel ones, and provides innovative and new approaches that might lead to Green's functions.

The 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.

Zielgruppe

Graduate Students, Researchers, and Lecturers in Mathematics, Finance and Engineering; Academic Libraries

Autoren/Hrsg.

Melnikov, Yuri A.

Melnikov, Max Y.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematik Interdisziplinär Finanz- und Versicherungsmathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure

Inhaltsverzeichnis

Frontmatter
Preface
Contents
Chapter 0. Introduction
Chapter 1. Green’s Functions for ODE
Chapter 2. The Laplace Equation
Chapter 3. The Static Klein–Gordon Equation
Chapter 4. Higher Order Equations
Chapter 5. Multi-Point-Posed Problems
Chapter 6. PDE Matrices of Green’s type
Chapter 7. Diffusion Equation
Chapter 8. Black–Scholes Equation
Appendix. Answers to Chapter Exercises
Bibliography
Index

Über Autor(innen)

Melnikov, Yuri A.
Yuri A. Melnikov,Middle Tennessee State University, Murfreesboro, USA;

Melnikov, Max Y.
Max Y.Melnikov, Cumberland University, Lebanon, Tennessee, USA.

Yuri A. Melnikov, Middle Tennessee State University, Murfreesboro, Tennessee, USA; Max Y. Melnikov, Cumberland University, Lebanon, Tennessee, USA.