Solving inverse nodal problem with spectral parameter in boundary conditions

Reconstruction of the nonlocal Sturm-Liouville operator with boundary conditions depending on the parameter

“…In 1997, Yang [35] obtained a definite algorithm for the solution of inverse nodal problems with separated boundary conditions. Later, similar results for various boundary conditions were obtained in (see [1,[4][5][6][7]10,11,[14][15][16][17][18][19]21,28,[30][31][32][36][37][38] and references therein). On the other hand, it can be said that the inverse nodal problem for nonlocal boundary conditions is a relatively new topic.…”

Solving an inverse nodal problem with Herglotz–Nevanlinna functions in boundary conditions using the second‐kind Chebyshev wavelets method

“…Therefore, in accordance with equality $$$ \omega =\tilde{\omega} $$$ and using formula (), we obtain $$$ {\int}_0^{\pi }q={\int}_0^{\pi}\tilde{q} $$$, and at last by using Theorem 1, we have $$$ q=\tilde{q} $$$ almost everywhere on $$$ \left(0,\pi \right) $$$. Therefore, the proof is completed (also see Akbarpoor et al 24 ). □…”

“…In this section, the SCW method is used to solve inverse nodal problems () and (), and accuracy of presented method is shown by providing a few numerical examples. In addition, the comparison of SCW method with Chebyshev interpolation method 24,26 can be seen in numerical examples. To get the results for the numerical examples, we use Matlab software program.…”

“…In 2007, Babolian and Fattahzadeh 23 considered Chebyshev wavelets method to get approximate solution of integral equations by considering 1st kind Chebyshev polynomials. Akbarpoor et al 24 studied the BVP () and () with $$$ {\delta}_k=0,k=1,2,\dots, d,{\Delta}_l=0,l=2,3,\dots, D $$$, and $$$ {h}_0={H}_0=0 $$$ and used FCW and Chebyshev interpolation methods to get solution of inverse nodal problem in 2019. Apart from these, there are some studies in the literature about similar numerical techniques 25–33 .…”

Numerical Solutions of Inverse Nodal Problems for a Boundary Value Problem

“…In recent years, some numerical methods have been studied to determine the approximation solution of 1st type of Fredholm integral equation by Rashed [24,25]; Maleknejad, Saeedipoor, and Dehbozorgi [26]; Zhou and Xu [27], or other works. The approximation solutions of the inverse nodal problem for differential operators were studied by Akbarpoor, Koyunbakan, and Dabbaghian [28]; Gulsen, Yilmaz, and Akbarpoor [29]; Neamaty, Akbarpoor, and Yilmaz [30], respectively. In this study, we compute the approximation solution of the inverse nodal problem of BVP L by the first kind Chebyshev wavelet method and apply the first kind Chebyshev wavelet method for solving this problem.…”