This paper describes a study of a class of algorithms for the floating-point divide and square root operations, based on the Newton-Raphson iterative method. The two main goals were: (1) Proving the IEEE correctness of these iterative floating-point algorithms, i.e. compliance with the IEEE-754 standard for binary floating-point operations [1]. The focus was on software driven iterative algorit...

A central problem of numerical analysis is the approximate evaluation of integrals or derivatives of functions. In more generality, this is the approximate evaluation of a linear functional defined on a space of functions. Users often just have values of a function u at scattered points x1, . . . ,xN in the domain Ω of u, and then the value λ (u) of a linear functional λ must be approximated vi...

The application of nonlinear schemes like dual time stepping as preconditioners in matrix-free Newton-Krylov-solvers is considered and analyzed. We provide a novel formulation of the left preconditioned operator that says it is in fact linear in the matrix-free sense, but changes the Newton scheme. This allows to get some insight in the convergence properties of these schemes which are demonstr...

and Applied Analysis 3 The class of Runge-Kutta methods with CQ formula has been applied to delay-integro-differential equations by many authors (c.f. [18, 19]). For the CQ formula (9), we usually adopt the repeated trapezoidal rule, the repeated Simpson’s rule, or the repeated Newton-cotes rule, and so forth, denote η = max{?̃? 0 , ?̃? 1 , . . . , ?̃? m }. It should be pointed out that the adopte...

One 3-D transient temperature field model for a thin uniform plate caused by moving laser heat source is described in present study. The with power density Gaussian-distribution form considered when finite-thin heated. By using the separate variable method and Newton-Cotes method, semi-analytical solution of conduction equation finite obtained. Numerical results show that effect distribution, s...

Aims. We observed the high redshift (z = 3.969) GRB 050730 with Swift and XMM-Newton to study its prompt and afterglow emission. Methods. We carried out a detailed spectral and temporal analysis of Swift and XMM-Newton observations. Results. The X–ray afterglow of GRB 050730 was found to decline with time with superimposed intense flaring activity that extended over more than two orders of magn...

Nonlinear differential-algebraic equations (DAE) are typically solved using implicit stiff solvers based on backward difference formula or RADAU formula, requiring a Newton-Raphson approach for the nonlinear equations or using Rosenbrock methods specifically designed for DAEs. Consistent initial conditions are essential for determining numeric solutions for systems of DAEs. Very few systems of ...

Purpose – The purpose of this work is to study the flow of mixed convection and mass transfer of a steady laminar boundary layer about an isothermal vertical flat plate embedded in a non-Darcian porous medium in the presence of chemical reaction and viscous dissipation effects. Design/methodology/approach – The governing partial differential equations are converted into ordinary differential eq...

Christopher K. Newman, Dana A. Knoll, T-3 Physics-based preconditioning is a highly successful approach for multiple-time-scale problems where an accurate simulation is desired on the dynamical time scale. In our research we are developing physics-based preconditioners for ocean simulation based on barotropic-baroclinic splitting. Our approach is a fully implicit, fully coupled time integration...

We generalize purity of the Newton stratification to purity for a single break point of the Newton point in the context of local G-shtukas respectively of elements of the loop group of a reductive group. As an application we prove that elements of the loop group bounded by a given dominant coweight satisfy a generalization of Grothendieck’s conjecture on deformations of p-divisible groups with ...