We consider the Sturm–Liouville operator perturbed by a convolution integral on finite interval with Dirichlet boundary conditions and discontinuity in middle of interval. study inverse problem recovering term from spectrum. The is reduced to solving so-called main nonlinear equation singularity. To derive this equation, we do detailed analysis kernels transformation operators for integro-diffe...

This paper deals with the discrete system being finite-difference approximation of Sturm–Liouville problem frozen argument. The inverse theory is developed for this system. We describe two principal cases: degenerate and non-degenerate. For these cases, appropriate problems statements are provided, uniqueness theorems proved, reconstruction algorithms obtained. Moreover, relationship between ei...

Abstract. We introduce a variational algorithm, which solves the classical inverse Sturm-Liouville problem when two spectra are given. In contrast to other approaches, it recovers the potential as well as the boundary conditions without a priori knowledge of the mean of the potential. Numerical examples show that the algorithm works quite reliable, even in the presence of noise. A proof of the ...

Abstract. We present a variational algorithm for solving the classical inverse Sturm-Liouville problem in one dimension when two spectra are given. All critical points of the least squares functional are at global minima, which justifies minimization by a (conjugate) gradient descent algorithm. Numerical examples show that the resulting algorithm works quite reliable without tuning for particul...

Abstract In this paper, the heat conduction equation for composite materials posed and solved. The inverse Boundary Value Problem (BVP) described By studying solving direct problem in materials, we can determine function spaces solve problem. Sturm-Liouville method was used to by reduce it integral first kind. value be formulated as an kind equations. discretization algorithm applied reformulat...

This study is on the fuzzy eigenvalues and fuzzy eigenfunctions of the Sturm-Liouville fuzzy problem with fuzzy eigenvalue parameter. We find fuzzy eigenvalues and fuzzy eigenfunctions of the problem under the approach of Hukuhara differentiability. We solve an example. We draw the graphics of eigenfunctions. We show that eigenfunctions are valid fuzzy functions or not.