International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 1, Pages 137-143
doi:10.1155/S0161171286000170
Finite difference methods for computing eigenvalues of fourth order boundary value problems
Department of Applied Mathematics, University of Manitoba, Winnipeg R3T 2N2, Manitoba, Canada
Received 7 September 1984
Copyright © 1986 Riaz A. Usmani. 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 brief report 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 linear differential equation y(4)+(p(x)−λq(x))y=0. These methods are derived from the formulah4y1(4)=(δ4−16δ6+7240δ8−…)yi.Numerical results are included to demonstrate practical usefulness of our methods.