Solving an Inverse Sturm-Liouville Problem by a Lie-Group Method

By Chein-Shan Liu. 2008

63 citations recorded by the source corpus.

Solving an inverse Sturm-Liouville problem requires a mathematical process to determine unknown function in the Sturm-Liouville operator from given data in addition to the boundary values. In this paper, we identify a Sturm-Liouville potential function by using the data of one eigenfunction and its corresponding eigenvalue, and identify a spatial-dependent unknown function of a Sturm-Liouville differential operator. The method we employ is to transform the inverse Sturm-Liouville problem into a parameter identification problem of a heat conduction equation. Then a Lie-group estimation method is developed to estimate the coefficients in a system of ordinary differential equations discretized from the heat conduction equation. Numerical tests confirm the accuracy and efficiency of present approach. Definite and random disturbances are also considered when comparing the present method with that by using a technique of numerical differentiation.

Subfields: Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/08d3083403bfe56f86e0a506d0edf3d99c8809bf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Chein-Shan Liu
2. Saeid Abbasbandy
3. Satya N. Atluri
4. Zhuojia Fu
5. Wen Chen

In Numerical Analysis

1. Mir Sajjad Hashemi
2. Saeid Abbasbandy
3. Chein-Shan Liu
4. Shijun Liao
5. Y. Tan
6. Shijun Liao
7. Tasawar Hayat
8. M. Noorani

Citations in the corpus

• The Lie-group shooting method for solving the Bratu equation (2011, background): “Recently, LGSM successfully applied to various problems [20–32] and some additional papers about GPS can be found in [33–35].”