International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 1, Pages 183-187
A relationship between the modified Euler method and
1Department of Mathematics, Colorado State University, Fort Collins 80521, Colorado, USA
2Department of Mathematics, Ashland College, Ashland 44805, Ohio, USA
Received 18 March 1984; Revised 14 November 1984
Copyright © 1985 Richard B. Darst and Thomas P. Dence. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Approximating solutions to the differential equation where by a generalization of the modified Euler method yields a sequence of approximates that converge to . Bounds on the rapidity of convergence are determined, with the fastest convergence occuring when the parameter value is , so the generalized method reduces to the standard modified Euler method. The situation is similarly examined when f is altered.