The high pressure behavior of the structural and electronic properties of KC1 is studied with use of the density functional pseudopotential method within local-density approximation. Atzero pressure, the rocksalt phase is found to be lower in energy than CsCl structure. However, we predict a phase transition into CsCI structure at a pressure of about 1.5 GPa. The calculated ground state pro...

We analyze the stability and functional superconvergence of discretizations diffusion problems with narrow-stencil second-derivative generalized summation-by-parts (SBP) operators coupled simultaneous approximation terms (SATs). Provided that primal adjoint solutions are sufficiently smooth SBP-SAT discretization is consistent, we show linear functionals associated steady problem superconverge ...

In this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable Taylor and weight function approximation. The method is based on Weerakoon-Fernando method [S. Weerakoon, G.I. Fernando, A variant of Newton's method with third-order convergence, Appl. Math. Lett. 17 (2000) 87-93]. The method is optimal, as it needs three evaluations per iterate,...

In this paper, a fractional degree cubic spline scheme is proposed and analyzed for order with the multi-term Riemann–Liouvile (R–L) derivatives. For integral differential equations, we handle continuity equations attain system of linear algebraic by using matrix method based on piecewise test functions. The to solve initial value problems approximate solution equation approximation Reimann–Lio...

We will start with a review of some calculus. We start with one dimension to give intuition for higher dimensions. Given a function from one variable to one variable, for example, f(x) = x, we can approximate it via its derivatives. The most trivial approximation is without derivatives: we can approximate f(x) near c by just the constant f(c). But if f is rapidly changing (has large derivative)...

In recent years, fractional reaction-diffusion models have been studied due to their usefulness and importance in many areas of mathematics, statistics, physics, and chemistry. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative. The resulting solutions spread faster than classical solutions and may exhibit asymmetry, dependin...