Solving an inverse nodal problem with Herglotz–Nevanlinna functions in boundary conditions using the second‐kind Chebyshev wavelets method. (4th October 2022)

• Record Type: Journal Article
• Authors: Akbarpoor Kiasary, Shahrbanoo; Yilmaz, Emrah
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 4(2023)
• Page Start: 4437
• Page End: 4448
• Publication Date: 2022-10-04
• Subjects: inverse nodal problem -- second‐kind Chebyshev wavelets method -- Sturm–Liouville equation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8768
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This study considers Sturm–Liouville (S–L) equation with a special function which includes spectral parameter at boundary conditions and expresses asymptotic forms of inverse problem solution, nodal points, and lengths. Furthermore, it proves some uniqueness theorems. Doing this, approximate solution of inverse S–L problem is obtained by second‐kind Chebyshev polynomials whereby the second‐kind Chebyshev wavelets (SCW) method is used to solve these types of problems. Finally, effectiveness of the method is demonstrated in a few examples.