Mathematical Problems in Engineering
Volume 6 (2000), Issue 1, Pages 85-97

Direct method for variational problems via hybrid of block-pulse and chebyshev functions

Mohsen Razzaghi1,2 and Hamid-Reza Marzban2

1Department of Mathematics and Statistics, Mississippi State University, P.O. Box MA, 39762, MS, USA
2Department of Mathematics, Amirkabir University, Tehran, Iran

Received 21 June 1999; Revised 3 November 1999

Copyright © 2000 Mohsen Razzaghi and Hamid-Reza Marzban. 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.


A direct method for finding the solution of variational problems using a hybrid function is discussed. The hybrid functions which consist of block-pulse functions plus Chebyshev polynomials are introduced. An operational matrix of integration and the integration of the cross product of two hybrid function vectors are presented and are utilized to reduce a variational problem to the solution of an algebraic equation. Illustrative examples are included to demonstrate the validity and applicability of the technique.