Introduction to Numerical Analysis and Scientific Computing

Chapter 7

Numerical Solutions of Ordinary Differential Equations (ODEs)

7.1Introduction

7.2Analytic Solutions to ODEs

7.3Mathematical Settings for Numerical Solutions to ODEs

7.4Explicit Runge-Kutta Schemes

7.4.1Euler Explicit Method

7.4.2Second-Order Explicit Runge-Kutta Methods

7.4.3General Explicit Runge-Kutta Methods

7.4.4Control of the Time-Step Size

7.5Adams Multistep Methods

7.5.1Adams Schemes of Order 1

7.5.2Adams Schemes of Order 2

7.5.3Adams Schemes of Order 3

7.5.4Adams Methods of Order 4

7.6Multistep Backward Difference Formulae

7.7Approximation of a Two-Points Boundary Value Problem

7.8Exercises

7.9Computer Exercises

7.1 Introduction

Differential equations involve the dependence of some variable y(t) with respect to an independent ...