Related papers: Efficient resolution of the Colebrook equation
The Colebrook equation is a popular model for estimating friction loss coefficients in water and gas pipes. The model is implicit in the unknown flow friction factor f. To date, the captured flow friction factor f can be extracted from the…
The function $y = g(x) = \mathrm{log}\big(W(e^x)\big)$, where $W()$ denotes the Lambert W function, is the solution to the equation $y + e^y = x$. It appears in various problem situations, for instance the calculation of current-voltage…
Empirical Colebrook equation from 1939 is still accepted as an informal standard to calculate friction factor during the turbulent flow through pipes from smooth with almost negligible relative roughness to the very rough inner surface. The…
In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
In computational molecular science, calculation of electrostatic interactions involving charged atoms - the strongest interactions in condensed phases, is a major bottleneck. We propose a quantum-classical algorithm for fast, yet, accurate…
Solutions to a wide variety of transcendental equations can be expressed in terms of the Lambert $\mathrm{W}$ function. The $\mathrm{W}$ function, occurring frequently in applications, is a non-elementary, but now standard mathematical…
This paper introduces a new numerical method for approximating the Lambert W function in the real domain. The method transforms the function into a simpler form that allows iterative refinement of an initial guess. Two iterative strategies…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
The Lambert W function has utility for solving various exponential and logarithmic equations arranged in the form of $g(x)e^{g(x)}$. Using the Lambert W function and tetration, a variety of categorized inversion formulas are presented.…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
The Colebrook-White equation is the widely used basis for the calculation of the friction factor lambda for flows in pipes and ducts. Because this equation is implicit in lambda, many solutions have been developed to ease the calculation in…
Using only a limited number of computationally expensive functions, we show a way how to construct accurate and computationally efficient approximations of the Colebrook equation for flow friction. The presented approximations are based on…
We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…
We present a MATLAB function for the numerical evaluation of the Faddeyeva function w(z). The function is based on a newly developed accurate algorithm. In addition to its higher accuracy, the software provides a flexible accuracy vs…
We describe an algorithm to evaluate all the complex branches of the Lambert W function with rigorous error bounds in interval arithmetic, which has been implemented in the Arb library. The classic 1996 paper on the Lambert W function by…
We study the iterative algorithm proposed by S. Armstrong, A. Hannukainen, T. Kuusi, J.-C. Mourrat to solve elliptic equations in divergence form with stochastic stationary coefficients. Such equations display rapidly oscillating…
In this work we describe a fast and stable algorithm for the computation of the orthogonal moments of an image. Indeed, orthogonal moments are characterized by a high discriminative power, but some of their possible formulations are…
This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…