Use of a shooting method to compute eigenvalues of fourth-order two-point boundary value problems
type: Item
instance of: scholarly article
title: Use of a shooting method to compute eigenvalues of fourth-order two-point boundary value problems
zbMATH Open document ID: 0793.65064
DOI: 10.1016/0377-0427(93)90065-J
published in: Journal of Computational and Applied Mathematics
publication date: 1994-08-08T00:00:00Z
review text: It is shown how the shooting method (known for solving regular noneigenvalue type two-point boundary value problems) can also be used for solving eigenvalue problems related to fourth-order ordinary differential equations. Only four first-order equations, obtained after rewriting the fourth-order equation, have to be integrated from one end of the shooting range to the other. In the first stage of the procedure approximations to the required eigenvalues are obtained by finding a least-squares solution for various eigenvalues starting with small values near zero and stepping forward to cover the range of interest. The second stage consists of a Newton procedure to compute accurately the required eigenvalue and the corresponding eigenvector. Newton iterations for the first and fifth eigenvalues are tabulated.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 34L15
zbMATH DE Number: 490556
zbMATH Keywords: shooting method
zbMATH Keywords: eigenvalue problems
zbMATH Keywords: fourth-order ordinary differential equations
zbMATH Keywords: least-squares solution
author: Dixon J. Jones
MaRDI profile type: Publication
cites work: A New Fourth-order Finite-difference Method for Computing Eigenvalues of Fourth-order Two-point Boundary-value Problems
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cites work: A five-diagonal finite-difference method based on mixed-type interpolation for computing eigenvalues of fourth-order two-point boundary-value problems
description: scientific article; zbMATH DE number 490556