Green's Functions: Construction and Applications

Yuri A. Melnikov; Max Y. Melnikov

Published by De Gruyter 2012

Green's Functions

Construction and Applications

Yuri A. Melnikov and Max Y. Melnikov

Volume 42 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110253399

Overview
Contents

About this book

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.

Author / Editor information

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

Reviews

"[...] the book is a useful source for everyone who is studying or working in fields of science, finance, or engineering that involve practical solutions of partial differential equations."
L'Enseignement Mathématique 2/2012

"The monograph is a valuable source to any researcher or postgraduate student working in applied sciences or engineering that concern practical solutions of partial or ordinary differential equations."
Marius Ghergu, Zentralblatt für Mathematik

Supplementary Materials

Contents

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	i
Preface Requires Authentication Unlicensed Licensed Download PDF	vii
Contents Requires Authentication Unlicensed Licensed Download PDF	xi
Chapter 0. Introduction Requires Authentication Unlicensed Licensed Download PDF	1
Chapter 1. Green’s Functions for ODE Requires Authentication Unlicensed Licensed Download PDF	9
Chapter 2. The Laplace Equation Requires Authentication Unlicensed Licensed Download PDF	55
Chapter 3. The Static Klein–Gordon Equation Requires Authentication Unlicensed Licensed Download PDF	130
Chapter 4. Higher Order Equations Requires Authentication Unlicensed Licensed Download PDF	167
Chapter 5. Multi-Point-Posed Problems Requires Authentication Unlicensed Licensed Download PDF	226
Chapter 6. PDE Matrices of Green’s type Requires Authentication Unlicensed Licensed Download PDF	265
Chapter 7. Diffusion Equation Requires Authentication Unlicensed Licensed Download PDF	317
Chapter 8. Black–Scholes Equation Requires Authentication Unlicensed Licensed Download PDF	362
Appendix. Answers to Chapter Exercises Requires Authentication Unlicensed Licensed Download PDF	402
Bibliography Requires Authentication Unlicensed Licensed Download PDF	421
Index Requires Authentication Unlicensed Licensed Download PDF	427

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Graduate Students, Researchers, and Lecturers in Mathematics, Finance and Engineering; Academic Libraries
Pages
- Front matter: 12
- Main content: 435
Illustrations
- Illustrations: 46
Keywords: Green's Function; Partial Differential Equation; Elliptic; Parabolic

eBook

Published: April 2, 2012
ISBN: 9783110253399

Hardcover

Published: March 15, 2012
ISBN: 9783110253023