International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 577-584
One-dimensional adaptive grid generation
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
Received 1 November 1995; Revised 8 May 1996
Copyright © 1997 Ahmed M. M. Khodier and Adel Y. Hassan. 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.
In this work, we give an adaptive grid generation method which allows a single point to be
added in the regions of large variation. This method uses a quadrature rule as a weight function. Our
weight function measures the variation of the solution function on each subinterval of the solution domain.
The method is applied to obtain the numerical solutions of some differential equations. A comparison of
the numerical solution obtained by this method and other methods is given.