In:
AIMS Mathematics, American Institute of Mathematical Sciences (AIMS), Vol. 7, No. 5 ( 2022), p. 7528-7551
Abstract:
〈abstract〉〈p〉An efficient spectral method is proposed for a new Steklov eigenvalue problem in inverse scattering. Firstly, we establish the weak form and the associated discrete scheme by introducing an appropriate Sobolev space and a corresponding approximation space. Then, according to the Fredholm Alternative, the corresponding operator forms of weak formulation and discrete formulation are derived. After that, the error estimates of approximated eigenvalues and eigenfunctions are proved by using the spectral approximation results of completely continuous operators and the approximation properties of orthogonal projection operators. We also construct an appropriate set of basis functions in the approximation space and derive the matrix form of the discrete scheme based on the tensor product. In addition, we extend the algorithm to the circular domain. Finally, we present plenty of numerical experiments and compare them with some existing numerical methods, which validate that our algorithm is effective and high accuracy.〈/p〉〈/abstract〉
Type of Medium:
Online Resource
ISSN:
2473-6988
DOI:
10.3934/math.2022423
Language:
Unknown
Publisher:
American Institute of Mathematical Sciences (AIMS)
Publication Date:
2022
detail.hit.zdb_id:
2917342-5
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