Abstract
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.
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References
Agarwal, R.P., Regan, D.O.: Ordinary and Partial Differential Equations. Springer (2009)
Attili, B., Lesnic, D.: An efficient method for computing eigenelements of Sturm-Liouville fourth-order boundary value problems. Appl. Math. Comput. 182(2), 1247–1254 (2006)
Chapra, S.C., Canale, R.P.: Numerical Methods for Engineers. McGraw-Hill (2010)
EI-Gamel, M., Sameeh, M.: An efficient technique for Finding the Eigenvalues of fourth-order Sturm-Liouville problems. Appl. Math. 3, 920–925 (2012)
Greenberg, L., Marletta, M.: Algorithm 775: The code SLEUTH for solving fourth-order Sturm-Liouville problems. ACM Trans. Math. Softw. 23(4), 453–493 (1997)
Syam, M., Siyyam, H.: An efficient technique for finding the Eigenvalues of fourth-order Sturm-Liouville problems. Chaos Solitons Fractals 39, 659–665 (2009)
Acknowledgements
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).
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Attary, M., Agarwal, P. (2019). An Effective Numerical Technique Based on the Tau Method for the Eigenvalue Problems. In: Agarwal, P., Baleanu, D., Chen, Y., Momani, S., Machado, J. (eds) Fractional Calculus. ICFDA 2018. Springer Proceedings in Mathematics & Statistics, vol 303. Springer, Singapore. https://doi.org/10.1007/978-981-15-0430-3_12
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DOI: https://doi.org/10.1007/978-981-15-0430-3_12
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