ABSTRACT
The data set used to illustrate subroutine midpt is taken from Example 7.12. The output generated by the extrapolated modified midpoint method program is presented in Output 7.2.
Output 7.2 Solution by the extrapolated modified midpoint method
n tn yn, O(h**2) O(h**4) O(h**6) O(h**8)
7.15.3 The Fourth-Order Adams-Bashforth-Moulton Method The general algorithm for the fourth-order Adams-Bashforth-Moulton method is given by Eg. (7.236):
(7.358a)
(7.358b)
A FORTRAN subroutine, subroutine abm, for implementing the procedure is presented in Program 7.3. Subroutine abm works essentially like subroutine rk discussed in Section 7.15.1, except the fourth-order Adams-Bashforth-Moulton method is used instead of the fourth-order Runge-Kutta method. Program main defines the data set and prints it, calls subroutine abm to implement the solution, and prints the solution. Only the statements in program main which are different from the statements in program main in Section 7.15.1 are presented.
