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Hyers-Ulam Stability of Ordinary Differential Equations (Hardcover)
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Hyers-Ulam Stability of Ordinary Differential Equations (Hardcover)
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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:
The state-of-art is pure analysis with background functional
analysis. 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.
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