AN EFFICIENT NUMERICAL METHOD BASED ON LEGENDRE-GALERKIN APPROXIMATION FOR THE STEKLOV EIGENVALUE PROBLEM IN SPHERICAL DOMAIN

Ting Tan; Jing An

doi:10.11948/20180104

2021 Volume 11 Issue 2

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Ting Tan, Jing An. AN EFFICIENT NUMERICAL METHOD BASED ON LEGENDRE-GALERKIN APPROXIMATION FOR THE STEKLOV EIGENVALUE PROBLEM IN SPHERICAL DOMAIN[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 587-601. doi: 10.11948/20180104

Citation:

Ting Tan, Jing An. AN EFFICIENT NUMERICAL METHOD BASED ON LEGENDRE-GALERKIN APPROXIMATION FOR THE STEKLOV EIGENVALUE PROBLEM IN SPHERICAL DOMAIN[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 587-601. doi: 10.11948/20180104

AN EFFICIENT NUMERICAL METHOD BASED ON LEGENDRE-GALERKIN APPROXIMATION FOR THE STEKLOV EIGENVALUE PROBLEM IN SPHERICAL DOMAIN

Ting Tan¹,
Jing An^1, ,

1.
School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China

Corresponding author: Email address: aj154@163.com(J. An)

Abstract

Abstract

We present in this paper an efficient numerical method based on Legendre-Galerkin approximation for the Steklov eigenvalue problem in spherical domain. Firstly, by means of spherical coordinate transformation and spherical harmonic expansion, the original problem is reduced to a sequence of equivalent one-dimensional eigenvalue problems that can be solved individually in parallel. Through the introduction of the appropriate weighted Sobolev spaces, the weak form and corresponding discrete scheme are established for each one-dimensional eigenvalue problem. Then from the approximate property of orthogonal polynomials in the weighted Sobolev spaces, we prove the error estimates of approximate eigenvalues for each one dimensional eigenvalue problem. Finally, some numerical examples are provided to illustrate the validity of our algorithms.
- Steklov eigenvalue problem /
- Legendre-Galerkin approximation /
- weighted Soblev space /
- error estimation /
- spherical domain
MSC: 65N35, 65N25

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References

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