Description
Book SynopsisODEsAn Introduction.- Euler's Method.- The Taylor Series Method.- Linear Multistep MethodsI: Construction and Consistency.- Linear Multistep MethodsII: Convergence and Zero-Stability.- Linear Multistep MethodsIII: Absolute Stability.- Linear Multistep MethodsIV: Systems of ODEs.- Linear Multistep MethodsV: Solving Implicit Methods.- RungeKutta MethodI: Order Conditions.- Runge-Kutta MethodsII Absolute Stability.- Adaptive Step Size Selection.- Long-Term Dynamics.- Modified Equations.- Geometric Integration Part IInvariants.- Geometric Integration Part IIHamiltonian Dynamics.- Stochastic Differential Equations.
Trade ReviewFrom the reviews:
“This book by Griffiths (Univ. of Dundee, UK) and Higham (Univ. of Strathclyde, UK) introduces the fields of numerical analysis and scientific computation. … Overall, there are many examples and exercises for students to read and try. … The work is very readable for an introductory course. An undergraduate who has completed at least the full calculus sequence should find the material interesting and accessible. Summing Up: Recommended. Lower-division undergraduates.” (S. L. Sullivan, Choice, Vol. 48 (10), June, 2011)
“There is a place for an elementary text that concentrates on the mathematical aspects while still referring to the applications of initial-value ODEs, and have set out to produce such a book. … Each chapter ends with a set of graded exercises … . In addition, there are worked examples throughout the book that illustrate the important ideas being covered. … a preparatory text for students taking a graduate course in numerical analysis. … this book is very well suited to its intended purpose.” (Philip W. Sharp, Mathematical Reviews, Issue 2012 g)
“This book provides material for a first typical course introducing numerical methods for initial-value ordinary differential equations but also highlights some new and emerging themes. … The authors include a wealth of theoretical and numerical examples that motivate and illustrate the fundamental ideas … . Although the book is aimed to be used by undergraduate students I felt that it might well be of interest to academic teachers in the field. … I highly recommend the book … .” (Rolf Dieter Grigorieff, Zentralblatt MATH, Vol. 1209, 2011)
“This textbook introduces undergraduates in mathematics, engineering and the physical sciences to the use of numerical methods for solving ordinary differential equations. … The primary practical goal of the book is to show students what’s going on inside scientific computing software, and to give them a sense of the strengths and limitations of numerical methods. … This is an attractive, very readable introduction to the subject for students … .” (William J. Satzer, The Mathematical Association of America, May, 2011)
Table of ContentsODEs—An Introduction.- Euler’s Method.- The Taylor Series Method.- Linear Multistep Methods—I: Construction and Consistency.- Linear Multistep Methods—II: Convergence and Zero-Stability.- Linear Multistep Methods—III: Absolute Stability.- Linear Multistep Methods—IV: Systems of ODEs.- Linear Multistep Methods—V: Solving Implicit Methods.- Runge–Kutta Method—I: Order Conditions.- Runge-Kutta Methods–II Absolute Stability.- Adaptive Step Size Selection.- Long-Term Dynamics.- Modified Equations.- Geometric Integration Part I—Invariants.- Geometric Integration Part II—Hamiltonian Dynamics.- Stochastic Differential Equations.
