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MULTISTEP METHODS All of the methods we have studied until now are ex-
 

Summary: MULTISTEP METHODS
All of the methods we have studied until now are ex-
amples of one-step methods. These methods use one
past value of the numerical solution, call it yn, in order
to compute a new value yn+1. Multistep methods use
more than one past value, and these are often more
e cient than the earlier methods. For example,
yn+1 = yn+
h
2
[3f(xn; yn) f(xn 1; yn 1)] ; n 1
(1)
is an explicit, stable, second order method with trun-
cation error of size O h3 . We derive it below.
Multistep methods can be derived in a number of
ways, but the most popular methods are derived most
easily using numerical interpolation and numerical in-
tegration.
Integrate the equation
Y 0(x) = f (x; Y (x)) (2)

  

Source: Atkinson, Kendall - Departments of Computer Science & Mathematics, University of Iowa

 

Collections: Computer Technologies and Information Sciences