Numerical investigation of the inverse nodal problem by Chebisyhev interpolation method

Abstract

In this study, we deal with the inverse nodal problem for Sturm-Liouville equation with eigenparameter-dependent and jump conditions. Firstly, we obtain reconstruction formulas for potential function, q, under a condition and boundary data, α, as a limit by using nodal points to apply the Chebyshev interpolation method. Then, we prove the stability of this problem. Finally, we calculate approximate solutions of the inverse nodal problem by considering the Chebyshev interpolation method. We then present some numerical examples using Matlab software program to compare the results obtained by the classical approach and by Chebyshev polynomials for the solutions of the problem.

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

“…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.…”

“…Apart from these, there are some studies in the literature about similar numerical techniques. [25][26][27][28][29][30][31][32][33] The rest of the work will continue as follows. In Section 2, we denote asymptotic forms of eigenvalues, nodal points, and lengths of (1) and ( 2) and prove the uniqueness theorems.…”

“…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 . The rest of the work will continue as follows.…”

Inverse fractional Sturm‐Liouville problem with eigenparameter in the boundary conditions

“…The concept of inverse problem is defined as finding the coefficients of the equation and the constants in the conditions by using eigenparameters in the differential Sturm‐Liouville problem ( SLP ). The solution of this type of problems is possible in many ways, and the results have been obtained by many authors 1–10 . Since differential equations are considered as a model in physics, engineering, and biology, fractional differential equations, especially the Sturm‐liouville equation, have an important role in the literature.…”

“…The solution of this type of problems is possible in many ways, and the results have been obtained by many authors. [1][2][3][4][5][6][7][8][9][10] Since differential equations are considered as a model in physics, engineering, and biology, fractional differential equations, especially the Sturm-liouville equation, have an important role in the literature.…”