An Effective Numerical Technique Based on the Tau Method for the Eigenvalue Problems

  • Maryam Attary
  • Praveen AgarwalEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 303)


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.


Eigenvalue problems Legendre polynomials Numerical treatment 

Mathematics Subject Classifications

65L15 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. 1.
    Agarwal, R.P., Regan, D.O.: Ordinary and Partial Differential Equations. Springer (2009)Google Scholar
  2. 2.
    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)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Chapra, S.C., Canale, R.P.: Numerical Methods for Engineers. McGraw-Hill (2010)Google Scholar
  4. 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
  5. 5.
    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)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Syam, M., Siyyam, H.: An efficient technique for finding the Eigenvalues of fourth-order Sturm-Liouville problems. Chaos Solitons Fractals 39, 659–665 (2009)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Karaj BranchIslamic Azad UniversityKarajIran
  2. 2.Department of MathematicsANAND International College of EngineeringJaipurIndia
  3. 3.Department of MathematicsHarish Chandra Research InstituteJhunsiIndia
  4. 4.International Center for Basic and Applied SciencesJaipurIndia

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