Hyers-Ulam Stability of Ordinary Differential Equations
暫譯: 常微分方程的Hyers-Ulam穩定性
Tripathy, Arun Kumar
- 出版商: CRC
- 出版日期: 2021-05-25
- 售價: $6,190
- 貴賓價: 9.5 折 $5,881
- 語言: 英文
- 頁數: 228
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 0367636670
- ISBN-13: 9780367636678
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商品描述
Hyers-Ulam Stability of Ordinary Differential Equations undertakes an interdisciplinary, integrative overview of a kind of stability problem unlike the existing so called stability problem for Differential equations and Difference Equations. In 1940, S. M. Ulam posed the problem: When can we assert that approximate solution of a functional equation can be approximated by a solution of the corresponding equation before the audience at the University of Wisconsin which was first answered by D. H. Hyers on Banach space in 1941. Thereafter, T. Aoki, D. H. Bourgin and Th. M. Rassias improved the result of Hyers. After that many researchers have extended the Ulam's stability problems to other functional equations and generalized Hyer's result in various directions. Last three decades, this topic is very well known as Hyers-Ulam Stability or sometimes it is referred Hyers-Ulam-Rassias Stability. This book synthesizes interdisciplinary theory, definitions and examples of Ordinary Differential and Difference Equations dealing with stability problems.
The purpose of this book is to display the new kind of stability problem to global audience and accessible to a broader interdisciplinary readership for e.g those are working in Mathematical Biology Modeling, bending beam problems of mechanical engineering also, some kind of models in population dynamics. This book may be a starting point for those associated in such research and covers the methods needed to explore the analysis.
Features:
- A rich, unique synthesis of interdisciplinary findings and insights on resources.
- As we understand that the real world problem is heavily involved with Differential and Difference equations, the cited problems of this book may be useful in a greater sense as long as application point of view of this Hyers-Ulam Stability theory is concerned.
- Information presented in an accessible way for students, researchers, scientists and engineers.
商品描述(中文翻譯)
《常微分方程的Hyers-Ulam穩定性》對一種穩定性問題進行了跨學科的綜合概述，這種問題與現有的所謂微分方程和差分方程的穩定性問題不同。1940年，S. M. Ulam提出了這個問題：我們何時可以斷言一個泛函方程的近似解可以被對應方程的解所近似？這個問題在1941年由D. H. Hyers在巴拿赫空間中首次回答。此後，T. Aoki、D. H. Bourgin和Th. M. Rassias改進了Hyers的結果。隨後，許多研究者將Ulam的穩定性問題擴展到其他泛函方程，並在各個方向上推廣了Hyers的結果。在過去的三十年中，這個主題被廣泛稱為Hyers-Ulam穩定性，有時也稱為Hyers-Ulam-Rassias穩定性。本書綜合了與穩定性問題相關的常微分方程和差分方程的跨學科理論、定義和例子。
本書的目的是向全球讀者展示這種新型的穩定性問題，並使其對更廣泛的跨學科讀者群體可及，例如那些從事數學生物建模、機械工程中的彎曲梁問題以及某些人口動態模型的研究者。本書可能成為與此類研究相關的人的起點，並涵蓋探索分析所需的方法。
**特點：**
- 最先進的內容是純分析，背景為泛函分析。
- 對跨學科發現和資源的豐富、獨特的綜合。
- 我們理解現實世界的問題與微分方程和差分方程密切相關，本書所引用的問題在Hyers-Ulam穩定性理論的應用觀點上可能具有更大的意義。
- 以易於理解的方式呈現的信息，適合學生、研究人員、科學家和工程師。
作者簡介
Dr. Arun Kumar Tripathy, Reader, Department of Mathematics, Sambalpur University, Sambalpur-768019 is a known name in the literature of Oscillation Theory since last two decades. His contribution basically deals with the linear and nonlinear neutral equations in difference equations, differential equations as well as in Time scales of first, second fourth and higher order equations. It is almost important that this theory is a part of so called Dynamical Systems based on Qualitative Behaviour of Solutions Differential and Difference equations. Up to his credit, he has published seventy research papers in peer reviewed journals of international repute. Apart from that he has several international collaborators Prof. S. Pinelas (Portugal), Prof. E. Schmeidal (Poland), Prof. T. G. Baskar (USA) etc. He has been invited to give talks at several international conferences. He is a potential reviewer of many international journals. After completing successfully the two years Post-Doctoral Fellowship offered by National Board for Higher Mathematics, Dept of Atomic Energy, Mumbai, Govt of India, Dr Tripathy has started his teaching career in the year 2003 and till now it is a primary job. Besides this, research is his special interest and this interest has been continued since 19 years.
作者簡介(中文翻譯)
阿倫·庫馬·特里帕提博士（Dr. Arun Kumar Tripathy），現任印度桑巴爾普爾大學數學系的講師，已在振盪理論的文獻中享有盛名，已有二十年的歷史。他的研究主要涉及線性和非線性中性方程，涵蓋差分方程、微分方程以及一階、二階、四階及更高階的時間尺度方程。這一理論幾乎是所謂的基於解的質量行為的動態系統的一部分，涉及微分方程和差分方程。至今，他已在國際知名的同行評審期刊上發表了七十篇研究論文。此外，他還與多位國際合作者合作，包括葡萄牙的S. Pinelas教授、波蘭的E. Schmeidal教授、美國的T. G. Baskar教授等。他曾受邀在多個國際會議上發表演講，並且是許多國際期刊的潛在審稿人。在成功完成由印度政府原子能部高等數學國家委員會提供的兩年博士後研究獎學金後，特里帕提博士於2003年開始了他的教學生涯，至今仍是他的主要工作。除此之外，研究是他的特殊興趣，這一興趣已持續了19年。
