An Effective Numerical Technique Based on the Tau Method for the Eigenvalue Problems
We consider the (presumably new) effective numerical scheme based on the Legendre polynomials for an approximate solution of eigenvalue problems. First, a new operational matrix, which can be represented by a sparse matrix defined by using the Tau method and orthogonal functions. Sparse data is by nature more compressed and thus requires significantly less storage. A comparison of the results for some examples reveals that the presented method is convenient and effective, also we consider the problem of column buckling to show the validity of the proposed method.
KeywordsEigenvalue problems Legendre polynomials Numerical treatment
Mathematics Subject Classifications65L15 65L05 65L10 65N35.
This work was supported to the second author [P Agarwal] by the research grant supported by the Department of Science & Technology(DST), India (No:INT/RUS/RFBR/P-308) and Science & Engineering Research Board (SERB), India (No:TAR/2018/000001).
- 1.Agarwal, R.P., Regan, D.O.: Ordinary and Partial Differential Equations. Springer (2009)Google Scholar
- 3.Chapra, S.C., Canale, R.P.: Numerical Methods for Engineers. McGraw-Hill (2010)Google Scholar
- 4.EI-Gamel, M., Sameeh, M.: An efficient technique for Finding the Eigenvalues of fourth-order Sturm-Liouville problems. Appl. Math. 3, 920–925 (2012)Google Scholar