We first develop an efficient spectral-Galerkin method and an rigorous error analysis for the generalized eigenvalue problems associated to a transmission eigenvalue problem. Then, we present an iterative scheme, based on computation of the first transmission eigenvalue, to estimate the index of refraction of an inhomogeneous medium. We present ample numerical results to demonstrate the effecti...

An inverse spectral problem is studied for second-order differential operators on hedgehog-type graphs with standard matching conditions in internal vertices and with mixed boundary conditions in boundary vertices. We prove a uniqueness theorem of recovering the coefficients of differential equations and boundary conditions from the given spectral characteristics. AMS Subject Classifications: A...

We provide a complete spectral characterization of a new method of constructing isospectral (in fact, unitary) deformations of general Schrrdinger operators H =-d2/d.x 2 + V in L2(/l~). Our technique is connected to Dirichlet data, that is, the spectrum of the operator H D on L2((-~,x0)) @ L2((x0, oo)) with a Difichlet boundary condition at x 0. The transformation moves a single eigenvalue of H...

In this paper, we consider an inverse problem of linear heat equation with nonlinear boundary condition. We identify the temperature and the unknown radiation tern from an overspecified condition on the boundary

We present a spectral inverse model to estimate a smooth source function from a limited number of observations for an advection-diffusion problem. A standard least-square inverse model is formulated by using a set of Gaussian radial basis functions (GRBF) on a rectangular mesh system. Here, the choice of the collocation points is modeled as a random variable and the generalized polynomial chaos...