Overview
- Is a concise textbook of numerical solutions of both ordinary differential equations and delay DEs
- Provides readers with numerical algorithms and explicit illustrative figures
- Treats complex function theory in a manner that shows its usefulness
Part of the book series: UNITEXT (UNITEXT, volume 145)
Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Ordinary differential equations (ODEs) provide a strong mathematical tool to express a wide variety of phenomena in science and engineering. Along with its own significance, one of the powerful directions toward which ODEs extend is to incorporate an unknown function with delayed argument. This is called delay differential equations (DDEs), which often appear in mathematical modelling of biology, demography, epidemiology, and control theory. In some cases, the solution of a differential equation can be obtained by algebraic combinations of known mathematical functions. In many practical cases, however, such a solution is quite difficult or unavailable, and numerical approximations are called for. Modern development of computers accelerates the situation and, moreover, launches more possibilities of numerical means. Henceforth, the knowledge and expertise of the numerical solution of differential equations becomes a requirement in broad areas of science and engineering.
One might think that a well-organized software package such as MATLAB serves much the same solution. In a sense, this is true; but it must be kept in mind that blind employment of software packages misleads the user. The gist of numerical solution of differential equations still must be learned.
The present book is intended to provide the essence of numerical solutions of ordinary differential equations as well as of delay differential equations. Particularly, the authors noted that there are still few concise textbooks of delay differential equations, and then they set about filling the gap through descriptions as transparent as possible. Major algorithms of numerical solution are clearly described in this book. The stability of solutions of ODEs and DDEs is crucial as well. The book introduces the asymptotic stability of analytical and numerical solutions and provides a practical way to analyze their stability by employing a theory of complex functions.
Authors and Affiliations
About the authors
Professor Guang-Da Hu is a professor at Department of Mathematics, Shanghai University.
Bibliographic Information
Book Title: Numerical Analysis of Ordinary and Delay Differential Equations
Authors: Taketomo Mitsui, Guang-Da Hu
Series Title: UNITEXT
DOI: https://doi.org/10.1007/978-981-19-9263-6
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023
Softcover ISBN: 978-981-19-9262-9Published: 24 May 2023
eBook ISBN: 978-981-19-9263-6Published: 23 May 2023
Series ISSN: 2038-5714
Series E-ISSN: 2532-3318
Edition Number: 1
Number of Pages: VIII, 113
Number of Illustrations: 28 b/w illustrations, 9 illustrations in colour
Topics: Numerical Analysis, Analysis, Algorithms