Numerical Methods for Ordinary Differential Equations Initial Value Problems /

• Main Authors: Griffiths, David F. (Author), Higham, Desmond J. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London, 2010.
• Series: Springer Undergraduate Mathematics Series,
• Subjects: Mathematics.; Numerical analysis.; Numerical Analysis.; Numeric Computing.

Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sig...

Table of Contents:

• ODEs—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.