Numerical Computation of Sturm-Liouville Problem with Robin Boundary Condition
Creators
Description
The modelling of physical phenomena, such as the earth's free oscillations, the vibration of strings, the interaction of atomic particles, or the steady state flow in a bar give rise to Sturm- Liouville (SL) eigenvalue problems. The boundary applications of some systems like the convection-diffusion equation, electromagnetic and heat transfer problems requires the combination of Dirichlet and Neumann boundary conditions. Hence, the incorporation of Robin boundary condition in the analyses of Sturm-Liouville problem. This paper deals with the computation of the eigenvalues and eigenfunction of generalized Sturm-Liouville problems with Robin boundary condition using the finite element method. Numerical solution of classical Sturm–Liouville problem is presented. The results show an agreement with the exact solution. High results precision is achieved with higher number of elements.
Files
10003055.pdf
Files
(458.2 kB)
| Name | Size | Download all |
|---|---|---|
|
md5:0b5553e48fe4258b4403a16ed09b878c
|
458.2 kB | Preview Download |
Additional details
References
- Sturm-Liouville problem, In Encyclopædia, 2015, Britannica. Retrieved from http://www.britannica.com/topic/Sturm-Liouville problem.
- A. Zettl, "Sturm-liouville theory", American Mathematical Soc., vol. 121, 2010.
- M. D. Milkhailov, & N. L. Vulchanov, "Computational procedure for Sturm-Liouville problems". Journal of Computational Physics, vol. 50 (3), 1983, 323-336.
- C. T. Fulton, & S. A. Pruess, "Eigenvalue and eigenfunction asymptotics for regular Sturm-Liouville problems", Journal of Mathematical Analysis and Applications, vol. 188 (1), 1994, pp. 297-340.
- Q. Kong, A. Zettl, Eigenvalues of regular Sturm–Liouville problems. Journal of differential equations, vol. 131(1), 1996, pp. 1-19.
- S. Abbasbandy, A. Shirzadi,, "A new application of the homotopy analysis method: Solving the Sturm–Liouville problems", Communications in Nonlinear Science and Numerical Simulation, vol. 16(1), 2011, pp. 112-126.
- Q. Kong, H. Wu, A. Zettl, "Dependence of the nth Sturm–Liouville eigenvalue on the problem", Journal of differential equations, vol. 156 (2), 1999, pp. 328-354.
- S. Pruess, Estimating the eigenvalues of Sturm-Liouville problems by approximating the differential equation. SIAM Journal on Numerical Analysis, 1973, vol. 10(1), pp. 55-68.
- M. Lakestani, M. Dehghan, "Numerical solution of fourth order integro differential equations using Chebyshev cardinal functions", International Journal of Computer Mathematics, vol. 87, 2010, pp. 1389-1394. [10] Q. M. Al-Mdallal, "On the numerical solution of fractional Sturm–Liouville problems", International Journal of Computer Mathematics, vol. 87 (12), 2010, pp. 2837-2845. [11] B. M. Levitan, "Inverse Sturm-Liouville Problems", 1987, VSP [12] W. O. Amrein, A. M. Hinz, D. B. Pearson, "Sturm-Liouville theory: past and present", Springer Science & Business Media., 2005. [13] D. W. Hahn, M. N. Ozisk, "Heat Conduction, 3rd edition". New York: Wiley. 2012, ISBN 978-0-470-90293-6.