This paper deals with the solution of the spherically symmetric time-dependent Hartree-Fock approximation applied to nuclear giant monopole resonances in the small amplitude regime. The problem is spatially unbounded as the resonance state is in the continuum. The practical requirement to perform the calculation in a finite-sized spatial region yields an artificial boundary, which is not presen...

We present a Bayesian framework for reconstruction of subsurface hydraulic properties from nonlinear dynamic flow data by imposing sparsity on the distribution of the solution coefficients in a compression transform domain. Sparse representation of the subsurface flow properties in a compression transform basis lends itself to a natural regularization approach, i.e. sparsity regularization, whi...

This paper discusses the multiscale method for the time-dependent Maxwell’s equations with memory effects in composite materials. The main difficulty is that one cannot use the usual multiscale asymptotic method (cf. [25, 4]) to solve this problem, due to the complication of the memory terms. The key steps addressed in this paper are to transfer the original integrodifferential equations to the...

Abstract The main aim of this article is to study a new generalizations the Gauss hypergeometric matrix and confluent functions by using two-parameter Mittag–Leffler function. In particular, we investigate certain important properties these extended such as integral representations, differentiation formulas, beta transform, Laplace transform. Furthermore, introduce an extension Jacobi orthogona...

We introduce the Laplace transform for an arbitrary time scale. Two particular choices of time scales, namely the reals and the integers, yield the concepts of the classical Laplace transform and of the classical Z-transform. Other choices of time scales yield new concepts of our Laplace transform, which can be applied to find solutions of higher order linear dynamic equations with constant coe...

Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects. Using equations, however, sometimes leads to solutions domain that are not readily invertible real by analytical means. Thus, we need numerical inversion methods convert obtained solution from a domain. In this paper, propose scheme based on inverse approximate fractal-fr...