In this paper, we present a numerical technique for performing Lie advection of arbitrary differential forms. Leveraging advances in high-resolution finite volume methods for scalar hyperbolic conservation laws, we first discretize the interior product (also called contraction) through integrals over Eulerian approximations of extrusions. This, along with Cartan’s homotopy formula and a discret...

An approximation is obtained for the recession of a sloping aquifer. The analytical approximation can provide a useful tool to analyze data and obtain physical properties of the aquifer. In contrast to the case of a horizontal aquifer, when plotting the time derivative of the flux versus the flux on a log scale, the result shows that the flux derivative reaches a minimum value and that the curv...

Nonstationary Gaussian process models can capture complex spatially varying dependence structures in spatial data. However, the large number of observations modern datasets makes fitting such computationally intractable with conventional dense linear algebra. In addition, derivative-free or even first-order optimization methods be slow to converge when estimating many parameters. We present her...

This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of random tangent vector field on unit sphere. The SPDE is governed by diffusion operator Lévy-type behaviour spatial solution, derivative in time depict intermittency its temporal and driven vector-valued Brownian motion sphere characterize long-range dependence. solution presented form Kar...

In this paper, an implicit difference scheme is proposed and analyzed for a class of nonlinear fourth-order equations with the multi-term Riemann–Liouvile (R–L) fractional integral kernels. For convection term, we handle implicitly attain system algebraic by using Galerkin method based on piecewise linear test functions. The terms are treated convolution quadrature. order to obtain fully discre...

Because optical diffusion imaging is a highly nonlinear inverse problem, iterative inversion algorithms based on the Born approximation have usually been employed as reconstruction technique, but convergence is slow, especially for high contrast parameter distributions. We show here that the slow convergence of the conventional algorithms is due to the linear integral operator derived by the Bo...

Local Derivative-Free Approximation of Computationally Expensive Posterior Densities Nikolay Bliznyuk a , David Ruppert b & Christine A. Shoemaker c a Department of Statistics, University of Florida, Gainesville, FL, 32611 b School of Operations Research and Information Engineering, Cornell University, Ithaca, NY, 14853 c School of Civil and Environmental Engineering, and School of Operations R...

in this paper, simultaneous control of source terms is considered in a vibrational string problem.in the considered problem, the terms to be controlled are the force and the initial velocity functions. we statethe generalized (weak) solution about the considered problem. the existence and uniqueness of the solutionfor optimal control problem is investigated. the frechet derivative of the functi...

Nowadays, fractional derivative is used to model various problems in science and engineering. In this paper, a new numerical method approximate the generalized Hattaf involving nonsingular kernel proposed. This included several forms existing literature such as Caputo–Fabrizio derivative, Atangana–Baleanu weighted derivative. The proposed based on Lagrange polynomial interpolation, it applied s...