International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 3, Pages 525-529
doi:10.1155/S0161171287000620

Two new finite difference methods for computing eigenvalues of a fourth order linear boundary value problem

Riaz A. Usmani1 and Manabu Sakai2

1Department of Applied Mathematics, University of Manitoba, Winnipeg R3T 2N2, Manitoba, Canada
2Department of Mathematics, University of Kagoshima, Kagoshima 890, Japan

Received 5 April 1985

Copyright © 1987 Riaz A. Usmani and Manabu Sakai. 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.

Abstract

This paper describes some new finite difference methods of order 2 and 4 for computing eigenvalues of a two-point boundary value problem associated with a fourth order differential equation of the form (py″)′​′+(q−λr)y=0. Numerical results for two typical eigenvalue problems are tabulated to demonstrate practical usefulness of our methods.