USING SEMI-ANALYTIC TECHNIQUE TO SOLVE SINGULAR QUADRATIC EIGENVALUE PROBLEMS
Luma. N. M. Tawfiq
Baghdad University, College of Education for Pure Science, Department of Mathematics.
Aseel Hisham
Baghdad University, College of Education for Pure Science, Department of Mathematics.
60-71
Vol: 5, Issue: 2, 2015
Receiving Date:
2015-02-26
Acceptance Date:
2015-03-28
Publication Date:
2015-04-30
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Abstract
This paper is concerned with a semi-analytic technique to find the solution of quadratic eigenvalue
problems for singular ordinary differential equations that arise in the areas of solid mechanics, acoustics
and coupled structural acoustics. The technique finds the eigenvalue and the corresponding nonzero
eigenvector which represent the solution of the problems in a certain domain. Illustration example is
presented, which provided to demonstrate the efficiency and accuracy of the proposed technique where
the suggested solution compared with other methods. Also, we propose a new formula developed to
estimate the error help reduce the accounts process and show the results are improved.The existing code
bvpsuite designed for the estimate the error of solution of boundary value problems was extended by a
model for the computation the estimate error for the solution of the problem in this paper.
Keywords:
Ordinary differential equation, Eigenvalue, Eigenvector, Interpolation polynomial, Quadratic eigenvalue problems.
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