In this manuscript, we study the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. By defining  a new Hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...

This paper considers a linear one dimensional inverse heat conduction problem with non constant thermal diffusivity and two unknown terms in a heated bar with unit length. By using the WKB method, the heat flux at the end of boundary and initial temperature will be approximated, numerically. By choosing a suitable parameter in WKB method the ill-posedness of solution will be improved. Finally, ...

We consider the inverse problem of identifying a Robin coefficient by performing measurements on some part of the boundary. By using a Kohn and Vogelius cost function, the inverse problem is turned into an optimisation one, which is proved to be stable with respect to the data. Robustness of the so obtained algorithm is also proved. Further investigations are related the recovery of the fast va...

the determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. for solving these ill-posed inverse problems, galerkin method based on sinc basis functions for space and time will be used. to solve the system of linear equation, a noise is imposed and tikhonove regularization is applied. by using a sensor located at a point in the domain of $x$, say $...

We prove the instability of averages of the conductivity in the inverse boundary value problem of Calderón, also known as the inverse conductivity problem or EIT.

Determining the shape of an inclusion within a conducting medium from voltage and current measurements on the accessible boundary of the medium can be modeled as an inverse boundary value problem for the Laplace equation. We present a solution method for such an inverse boundary value problem with a generalized impedance boundary condition on the inclusion via boundary integral equations. Both ...

A Class of new methods based on a septic non-polynomial spline function for the numerical solution one-dimensional Bratu's problem are presented. The local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. The inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. Associated boundary f...

In this manuscript, we consider the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. We prove by defining a new Hilbert space and using spectral data of a kind, the potential function can be uniquely determined by a set of value of eigenfunctions at an interior point and p...

This paper deals with the boundary value problem involving the differential equation begin{equation*}     ell y:=-y''+qy=lambda y,  end{equation*}  subject to the standard boundary conditions along with the following discontinuity  conditions at a point $ain (0,pi)$  begin{equation*}     y(a+0)=a_1 y(a-0),quad y'(a+0)=a_1^{-1}y'(a-0)+a_2 y(a-0), end{equation*} where $q(x),  a_1 , a_2$ are  rea...