Unformatted text preview: y locating the discontinuity and restarting the solution there is also simpler
with RungeKutta methods than with competing methods.
Implicit RungeKutta methods are useful when high accuracy and A or Lstability
are needed simultaneously. This occurs with problems where fy (t y) has eigenvalues with
large (neagative) real or imaginary parts. We will postpone a comparison of methods
for these problems until examining multistep methods in Chapter 5. At this time, we'll
note that software based on fth, seventh and ninthorder Radau methods 17] has
done extremely well when solving sti IVPs. The STRIDE software 6] based on SIRK
methods has been successful, but less so than the Radau methods. Problems 1. The aim of this problem is to write a subroutine or procedure for performing one
step of a fourthorder variable step RungeKutta method applied to vector IVPs of
the form
y = f (t y)
y(t0) = y0 :
0 1.1. Write a subroutine or procedure to perform one step of a fourthorder explicit
RungeKutta metho...
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This document was uploaded on 03/16/2014 for the course CSCI 6820 at Rensselaer Polytechnic Institute.
 Spring '14
 JosephE.Flaherty

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