Chapter 9
Collocation Methods
9.1 Introduction
Let's continue the discussion of collocation methods with the second-order linear BVP
Ly = y + p(x)y + q(x)y = r(x)
00
a<x<b
0
y(a) = A
(9.1.1a)
y(b) = B
Chapter 8
Finite Di erence Methods
8.1 Introduction
Let's continue the discussion of nite di erence procedures for two-point boundary value
problems that we began in Section 6.3 with a brief review of
Chapter 7
Initial Value Methods
7.1 Introduction
We'd like to extend the initial-value or shooting procedures to vector systems of m rstorder ODEs. However, before studying nonlinear problems, let's f
Part 3: Two-Point Boundary Value
Problems
1
2
Chapter 6
Fundamental Problems and Methods
6.1 Problems to be Solved
Several problems arising in science and engineering are modeled by di erential equati
Chapter 5
Multivalue or Multistep Methods
5.1 Introduction
One-step methods only require information about the solution at one time, say t = tn;1
to compute the solution at an advanced time t = tn. Af
Chapter 4
Extrapolation Methods
4.1 Polynomial and Rational Extrapolation
In Chapter 3, we used extrapolation as a tool to estimate the discretization errors of highorder Runge-Kutta methods. We learn
Chapter 3
One-Step Methods
3.1 Introduction
The explicit and implicit Euler methods for solving the scalar IVP
y = f (t y)
y(0) = y0:
0
(3.1.1)
have an O(h) global error which is too low to make them
Part 2: Initial Value Problems
1
2
Chapter 2
Introduction
2.1 The Explicit Euler Method: Convergence and
Stability
As an introductory example, we examine, perhaps, the simplest method for solving the
Part 1: Overview of Ordinary Di erential Equations
1
2
Chapter 1
Basic Concepts and Problems
1.1 Problems Leading to Ordinary Di erential Equations
Many scienti c and engineering problems are modeled