International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 577-584

One-dimensional adaptive grid generation

Ahmed M. M. Khodier and Adel Y. Hassan

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.