Numerical Inversion of the Laplace Transform with Applications to Partial Differential Equations PDF Download

Author: Paul Cyprian Messina
Publisher:
ISBN:
Category :
Languages : en
Pages : 52

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Author: Alan M. Cohen
Publisher: Springer Science & Business Media
ISBN: 0387688552
Category : Mathematics
Languages : en
Pages : 262

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Book Description
This book gives background material on the theory of Laplace transforms, together with a fairly comprehensive list of methods that are available at the current time. Computer programs are included for those methods that perform consistently well on a wide range of Laplace transforms. Operational methods have been used for over a century to solve problems such as ordinary and partial differential equations.

Author: Richard Bellman
Publisher: World Scientific
ISBN: 9789971966737
Category : Mathematics
Languages : en
Pages : 180

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Book Description
The classical theory of the Laplace Transform can open many new avenues when viewed from a modern, semi-classical point of view. In this book, the author re-examines the Laplace Transform and presents a study of many of the applications to differential equations, differential-difference equations and the renewal equation.

Author: N.W. McLachlan
Publisher: Courier Corporation
ISBN: 0486798232
Category : Mathematics
Languages : en
Pages : 241

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Book Description
Classic graduate-level exposition covers theory and applications to ordinary and partial differential equations. Includes derivation of Laplace transforms of various functions, Laplace transform for a finite interval, and more. 1948 edition.

Author: Dalpatadu
Publisher: Trafford Publishing
ISBN: 1490760695
Category : Mathematics
Languages : en
Pages : 172

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Book Description
One of the first applications of the modern Laplace transform was by Bateman in 1910 who used it to transform Rutherfords equations in his work on radioactive decay. The modeling of complex engineering and physical problems by linear differential equations has made the Laplace transform an indispensable mathematical tool for engineers and scientists. The method of Laplace transform for solving linear differential equations is very popular in the disciplines of electrical engineering, environmental engineering, hydrology, and petroleum engineering. This book presents some applications of Laplace transforms in these disciplines. Algorithms for the numerical inversion of Laplace transform are given, and a computer program in R for the Stehfest algorithm is included.

Author: Richard Bellman
Publisher:
ISBN:
Category : Invariant imbedding
Languages : en
Pages : 272

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Author: Morteza Shafii-Mousavi
Publisher: Research & Education Assoc.
ISBN: 9780738672458
Category : Mathematics
Languages : en
Pages : 132

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Book Description
REA’s Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Laplace Transforms includes the Laplace transform, the inverse Laplace transform, special functions and properties, applications to ordinary linear differential equations, Fourier transforms, applications to integral and difference equations, applications to boundary value problems, and tables.

Author: Peter K.F. Kuhfittig
Publisher: Springer Science & Business Media
ISBN: 1489922016
Category : Mathematics
Languages : en
Pages : 208

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Book Description
The purpose of this book is to give an introduction to the Laplace transform on the undergraduate level. The material is drawn from notes for a course taught by the author at the Milwaukee School of Engineering. Based on classroom experience, an attempt has been made to (1) keep the proofs short, (2) introduce applications as soon as possible, (3) concentrate on problems that are difficult to handle by the older classical methods, and (4) emphasize periodic phenomena. To make it possible to offer the course early in the curriculum (after differential equations), no knowledge of complex variable theory is assumed. However, since a thorough study of Laplace. transforms requires at least the rudiments of this theory, Chapter 3 includes a brief sketch of complex variables, with many of the details presented in Appendix A. This plan permits an introduction of the complex inversion formula, followed by additional applications. The author has found that a course taught three hours a week for a quarter can be based on the material in Chapters 1, 2, and 5 and the first three sections of Chapter 7. If additional time is available (e.g., four quarter-hours or three semester-hours), the whole book can be covered easily. The author is indebted to the students at the Milwaukee School of Engineering for their many helpful comments and criticisms.

Author: J. M. Greenberg
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: Dean G. Duffy
Publisher: CRC Press
ISBN: 1420035142
Category : Mathematics
Languages : en
Pages : 727

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Book Description
Transform methods provide a bridge between the commonly used method of separation of variables and numerical techniques for solving linear partial differential equations. While in some ways similar to separation of variables, transform methods can be effective for a wider class of problems. Even when the inverse of the transform cannot be found ana