Runge-Kutta method
The formula for the fourth order Runge-Kutta method (RK4) is given below. Consider the
problem
(
y 0 = f (t, y)
y(t0 ) =
Define h to be the time step size and ti = t0 + ih. Then the following formula
w0 =
k1 = hf (ti , wi )
k1
h
k2 =

4
Linear Multistep Methods
An important class of numerical methods for initial value problems is that of the linear multistep
methods. Assuming the solution has been computed for some number of time steps, the idea is to
use the last k step values to appr

Chapter 8
Runge-Kutta Methods
Main concepts: Generalized collocation method, consistency, order conditions
In this chapter we introduce the most important class of one-step methods that are generically
applicable to ODES (1.2). The formulas describing Run

Appendix A
Runge-Kutta Methods
The Runge-Kutta methods are an important family of iterative methods for the approximation of solutions of ODEs, that were develoved around 1900 by the german
mathematicians C. Runge (18561927) and M.W. Kutta (18671944). We

8.19: Multistep Methods
Multistep methods are methods, which require starting values from several
previous steps.
There are two important families of multistep methods
Adams methods (explicit: AdamsBashforth as predictor, implicit:
AdamsMoulton as correc

Linear Multistep Methods
Lei Liu
October 1, 2008
Model Problem
Linear Multistep Methods
Convergence Analysis
Application to A-D-R equation
Table of Contents
1
2
3
4
Model Problem
Linear Multistep Methods
Definition
The Order Conditions
Classification and