Computerized tomography requires customized numerical methods for the approximation of a bivariate target function f from a finite set of discrete Radon data, each of whose data samples represents one line integral of f . In standard reconstruction methods, specific assumptions concerning the distribution of the sample lines are usually made, e.g. by parallel line geometry. In relevant applicat...

The boundary value and expansion problems for the equation of the nth order with boundary conditions at two points have been studied by Birkhoff. t BocherJ has suggested the generalization of these results to the equation with auxiliary conditions at more than two points. Such generalization of the essential properties of the differential system has been carried out by the author, and in this p...

Ideally, discretization methods for propagating waves should combine both high resolution for smooth solutions and L1-stability for nonsmooth solutions. Hermite methods are high-order polynomialbased spectral element methods for hyperbolic systems with a number of unique properties. A Hermite method whose degrees-of-freedom are the coefficients of a tensor-product Taylor polynomial of degree m ...

Abstract. Three-dimensional (3D) stratigraphic modeling is capable of the shape, topology, and other properties strata in a digitalized manner. The implicit approach becoming mainstream for 3D modeling, which incorporates both off-contact strike dip directions on-contact occurrence information interface to estimate potential field (SPF) represent architectures strata. However, magnitudes SPF gr...

The aim of this paper is to carry out a rigorous error analysis for the Strang splitting Laguerre–Hermite/Hermite collocation methods for the time-dependent Gross–Pitaevskii equation (GPE). We derive error estimates for full discretizations of the three-dimensional GPE with cylindrical symmetry by the Strang splitting Laguerre–Hermite collocation method, and for the d-dimensional GPE by the Str...

A novel adaptive spectral method has been recently developed to numerically solve partial differential equations (PDEs) in unbounded domains. To achieve accuracy and improve efficiency, the relies on dynamic adjustment of three key tunable parameters: scaling factor, a displacement basis functions, expansion order. In this paper, we perform first numerical analysis using generalized Hermite fun...

This is the second part of a two-part paper on Birkhoff systems. A Birkhoff system is an algebra that has two binary operations · and +, with each being commutative, associative, and idempotent, and together satisfying x · (x + y) = x + (x · y). The first part of this paper described the lattice of subvarieties of Birkhoff systems. This second part continues the investigation of subvarieties of...

The convergence of a class of combined spectral-finite difference methods using Hermite basis, applied to the Fokker-Planck equation, is studied. It is shown that the Hermite based spectral methods are convergent with spectral accuracy in weighted Sobolev space. Numerical results indicating the spectral convergence rate are presented. A velocity scaling factor is used in the Hermite basis and i...