Numerical Analysis of Ordinary and Delay Differential Equations
Seiten
2023
|
1st ed. 2023
Springer Verlag, Singapore
978-981-19-9262-9 (ISBN)
Springer Verlag, Singapore
978-981-19-9262-9 (ISBN)
This book serves as a concise textbook for students in an advanced undergraduate or first-year graduate course in various disciplines such as applied mathematics, control, and engineering, who want to understand the modern standard of numerical methods of ordinary and delay differential equations. Experts in the same fields can also learn about the recent developments in numerical analysis of such differential systems.
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.
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.
Professor Taketomo Mitsui is currently Professor Emeritus at Nagoya University. Professor Guang-Da Hu is a professor at Department of Mathematics, Shanghai University.
Chapter 1. Introduction.- Chapter 2. Initial-value Problems.- Chapter 3. Runge-Kutta Methods for ODEs.- Chapter 4. Polynomial Interpolation.- Chapter 5. Linear Multistep Methods for ODEs.- Chapter 6. Analytical Theory of Delay Differential Equations.- Chapter 7. Numerical DDEs and Their Stability.- Bibliography.- References.
| Erscheinungsdatum | 15.06.2023 |
|---|---|
| Reihe/Serie | La Matematica per il 3+2 | UNITEXT ; 145 |
| Zusatzinfo | 9 Illustrations, color; 28 Illustrations, black and white; VIII, 113 p. 37 illus., 9 illus. in color. |
| Verlagsort | Singapore |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Informatik ► Theorie / Studium ► Algorithmen |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| ISBN-10 | 981-19-9262-2 / 9811992622 |
| ISBN-13 | 978-981-19-9262-9 / 9789811992629 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
IT zum Anfassen für alle von 9 bis 99 – vom Navi bis Social Media
Buch | Softcover (2021)
Springer (Verlag)
CHF 41,95
Interlingua zur Gewährleistung semantischer Interoperabilität in der …
Buch | Softcover (2023)
Springer Fachmedien (Verlag)
CHF 46,15
Eine Einführung mit Java
Buch | Hardcover (2020)
dpunkt (Verlag)
CHF 62,85
