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Volume 3, Issue 4, August 2014, Page: 117-120
A Variational Method in the Sturm-Liouville Problem with the Neumann and Dirichlet Boundary Values
Khapaeva Tatiana Mikhailovna, Department of Calculative Mathematic and Cybernatic, Moscow, Russia; Moscow State Lomonosov’s University, MSU, Moscow, Russia
Received: Jun. 4, 2014;       Accepted: Jul. 4, 2014;       Published: Jul. 20, 2014
DOI: 10.11648/j.acm.20140304.11      View  3291      Downloads  179
A variational method for calculation of the eigenfunctions and eigenvalues in the Sturm-Liouville problem with the Neumann boundary values is offered. The method is based on a functional, which is introduced in this work. An appropriate numerical algorithm is developed. Calculations for the three potentials are produced: sin((x-π)2/π), cos(4x) and the high not isosceles triangle. The method is applied to the Sturm-Liouville problem with the Dirichlet boundary values. Some suppositions about the inverse Sturm-Liouville problem are made.
Sturm-Liouville Problem, Neumann Boundary Values, Dirichlet Boundary Values, Eigenfunctions, Eigenvalues, Variational Method, Functional, Inversed Sturm-Liuville problem, Algorithm
To cite this article
Khapaeva Tatiana Mikhailovna, A Variational Method in the Sturm-Liouville Problem with the Neumann and Dirichlet Boundary Values, Applied and Computational Mathematics. Vol. 3, No. 4, 2014, pp. 117-120. doi: 10.11648/j.acm.20140304.11
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Borg G. “Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte”, Acta Mathematica, vol. 78, 1946, pp. 1–96
A. N. Tikhonov and V. Ya. Arsenin, “Methods for Solving Ill-Posed Problems”, Nauka, Moscow, 1986 [in Russian]
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