Numerical solutions to inverse nodal problems for the Sturm–Liouville operator and their applications.
學年 113
學期 1
出版（發表）日期 2025-01-13
作品名稱 Numerical solutions to inverse nodal problems for the Sturm–Liouville operator and their applications.
作品名稱（其他語言）
著者 Wang, Yu Ping; Tsai, Tzong-Mo; Akbarpoor, Shahrbanoo; Shieh, Chung-Tsun
單位
出版者
著錄名稱、卷期、頁數 Journal of Inverse and Ill-posed Problems 33( 2)， pp. 269-280.
摘要 In this paper, we apply numerical methods to study inverse nodal problems for the Sturm–Liouville operator. At first, we find an approximate function of the potential from the nodal points of the ( n + 1 ) -th eigenfunction and three constants via the second kind Chebyshev wavelet method (SCW). We have a sharp condition for uniform convergence of Chebyshev series and an error estimate between the approximate solution and exact solution of the potential. Then, a numerical example is provided to show that the approximate solutions become more accurate and the errors decrease as the values of n increase. Also, we show the comparison of SCW with Bernstein method. Finally, we present an application of numerical solutions to reconstruct the potential from parts of nodal set and its mean value. Compared with some well-known results, the nodal data used here is least.
關鍵字 Inverse nodal problem; Sturm–Liouville operator; SCW; application; uniqueness
語言 en
ISSN
期刊性質 國外
收錄於 SCI Scopus
產學合作
通訊作者 Y. P. Wang
審稿制度 是
國別 DEU
公開徵稿
出版型式 ,電子版,紙本
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