This page shows you how to use the Euler Method to numerically find position, velocity, and acceleration as a function of time.

Given an efficient numerical method and a supercomputer, differential algebra can be a powerful tool for the study of accelerator physics. ''ZLIB,'' which has a style similar to the numerical library ''IMSL,'' has been developed to offer efficient numeric...

The development of a shock-accelerated diffuse Helium cylindrical inhomogeneity is investigated using a new numerical method. The new algorithm is a higher-order Godunov implementation of the so-called multi-fluid equations. This system correctly models m...

A characteristic method for transport calculations in two-dimensional geometries has been developed as a part of the interface-current transport code TDT. A complete description of angular and spatial approximations, as well as numerical implementation is given. A new synthetic acceleration technique has also been developed based on ...

The purpose of the work is to investigate methods leading to the design of quartz crystal units that are stable with respect to mechanically induced vibration and acceleration. Numerous experimental and theoretical aspects of the reactions of a vibrating ...

The paper offers a comparative review of methods for accelerating the numerical convergence of Fourier series. The various reasons for which Fourier series either diverge or converge sufficiently slowly to render them useless for computation are discussed...

The purpose of these lectures is to survey the subject of spin dynamics in accelerators: to give a sense of the underlying physics, the typical analytic and numeric methods used, and an overview of results achieved. Consideration will be limited to electrons and protons. Examples of experimental and theoretical results in both linear ...

This work deals with the expansion by eigenfunctions of Dirac system. For accelerating the convergence of this kind of expansions a nonlinear method is suggested, based on Pade approximants. Asymptotic estimates of L{sub 2} errors are derived. Some numerical examples are presented.

The underlying unity of the numerous surveying computational methods is hidden by many practical differences in data acquisition. Traditional programming languages have added to the confusion by requiring programmers to describe the numeric data in very c...

In this work, the numerical solution to a few of the electrostatic problems is dealt with which have occured within the framework of the heavy ion accelerator project VICKSI. By means of these selected examples, the versatile applicability of the numerical method is to be demonstrated, and simultaneously ...

... Accelerators and Colliders; Beam Dynamics; Applications and New Methods of Acceleration; New Methods; Linear Accelerators and Pulsed Power ...

Hall thrusters are widely used as space electric propulsion devices. Due to the complex plasma phenomenon and high computation cost, currently it is difficult to fully simulate the real physical process in Hall thrusters. Recently, Szabo and Taccogna have proposed two different methods to simplify and accelerate the simulation, respectively. In this paper, ...

A simplified algorithm is described for the numerical solution of the Navier--Stokes equations. Because of its simple construction, the algorithm serves as a good introduction to numerical fluid dynamics as well as a basis for developing many kinds of new solution methods. To illustrate the flexibility of this algorithm, simple ...

The numerical application of the poligon method of Gans proved to be a simple and reliable procedure for the design of an accelerating tabe with an inhomogeneous field for use in high voltage generators. Calculations were made using this method in connection with an accelerating tube of ...

A new method for enhancing the convergence rate of iterative algorithms for the numerical integration of systems of partial differential equations was developed. It is termed the Distributed Minimal Residual (DMR) method and it is based on general Krylov ...

... warfare, joint planning, national and international ... Numerical Studies for the RAM Accelerator. ... Author : NAVAL RESEARCH LAB WASHINGTON DC ...

... in the Spiral Line Induction Accelerator ... Numerical Modelling of Intense Electron Beam Transport in the Spiral Line Induction Accelerator ...

... oblique detonations in the ram accelerator: Can the concept of using a stable, oblique detonation actually be viable for ram accelerators? ...

We present a new class of synthetic acceleration methods which can be applied to transport calculations regardless of geometry, discretization scheme, or mesh shape. Unlike other synthetic acceleration methods which base their acceleration on P1 equations, these methods use ...

A new class of synthetic acceleration methods, which can be applied to transport calculations regardless of geometry, discretization scheme, or mesh shape, is presented. Unlike other synthetic acceleration methods that base their acceleration on P/sub l/ equations, these ...

A number of numerical methods, including inverse iteration, method of successive linear problem and nonlinear Arnoldi algorithm, are studied in this paper to solve a large scale nonlinear eigenvalue problem arising from finite element analysis of resonant...

This paper discusses the following issues relating to solving partial differential equations on array processors: domain decomposition; Schwarz methods; numerical Schwarz methods; and Fourier frequency acceleration. 5 refs. (ERA citation 14:021588)

This study investigates two methods of increasing the rate of convergence of the two dimensional five point implicit finite difference representation of the diffusion equation of transient heat transfer. The two methods are adapted Wegstein and successive...

A method previously developed to obtain the parameters, fields, and losses for linear accelerator cells loaded with shaped drift tubes was used for those shapes generated by a two-charge pair located on the axis of the cell. The apcussed and numerical results are given. (M.C.G.)

COSMIC-RAY ACCELERATION AT ULTRARELATIVISTIC SHOCK WAVES: EFFECTS OF DOWNSTREAM SHORT-WAVE acceleration processes at relativistic shock waves with the method of Monte Carlo simulations applied to shocks: numerical -- MHD -- relativity -- shock waves 1. INTRODUCTION Realistic modeling of first-order Fermi cosmic

Shortages of {sup 99}Mo, the most commonly used diagnostic medical isotope, have caused great concern and have prompted numerous suggestions for alternate production methods. A wide variety of accelerator-based approaches have been suggested. In this paper we survey and compare the various accelerator-based ...

In this paper, a Newton-Multigrid method is presented to solve the numerical simulation of the slider air bearing. For each fixed attitude in the specified grid, the Newton method is used to achieve the pressure distribution of the slider by solving the generalized Reynolds equations discretized by the least square finite difference ...

... Title : ACCELERATION OF THE CONVERGENCE OF THE KACZMARZ METHOD AND ITERATED HOMOGENEOUS TRANSFORMATIONS. ...

of the Acoustical Society of America 1997; 102(2):926�932. 30. Shen L, Liu YJ. An adaptive fast multipole boundary December 2006 KEY WORDS: boundary element method; fast multipole method; 3-D electrostatic problems with thin beams and accelerated by the fast multipole method. Engineering Analysis with Boundary ...

A method is described for the calculation of aerodynamic loads on a horizontal axis wind turbine rotor. The method is based upon acceleration potential theory. An approximate solution of the boundary value problem has been obtained using a matched asymptotic expansion technique. Furthermore a numerical integration ...

A new nonlinear coarse-mesh rebalance (CMR) method is developed and tested to accelerate the one- and two-dimensional discrete ordinates neutron transport calculations. The method is based on rebalance factors that are angular dependent and defined on the coarse-mesh boundaries only. Unlike the conventional CMR ...

Numerical algorithms for PIC simulation of beam dynamics in a high intensity synchrotron on a parallel computer are presented. We introduce numerical solvers of the Laplace-Poisson equation in the presence of walls, and algorithms to compute tunes and twiss functions in the presence of space charge forces. The working code for the simulation here presented ...

The accelerated hazard model has been proposed for more than a decade. However, its application is still very limited, partly due to the complexity of the existing semiparametric estimation method. We propose a new semiparametric estimation method based on a kernel-smoothed approximation to the limit of a profile likelihood function of ...

Numerical-analytical method for calculating accelerating-focusng fields in structures with space-homogeneous quadrupolar focusing is described in short. Example of concrete realization of the method suggested for modeling of three-dimensional quasistation...

Changes in plasma parameters and projectile velocity and acceleration in a rail gun during the launch are investigated numerically. The method involves determining the velocity and magnetic induction using a difference scheme and an explicit nonlinear method with flow correction for calculating plasma density. The ...

Small sampling errors can have a large effect on numerically integrated waveforms. An example is the integration of acceleration to compute velocity and displacement waveforms. These large integration errors complicate checking the suitability of the acceleration waveform for reproduction on shakers. For waveforms typically used for ...

Convergence properties were investigated for the response matrix method with various finite-difference formulations that can be utilized in the nonlinear acceleration method. The nonlinear acceleration method is commonly used for the diffusion calculation with the advanced nodal ...

In this paper, a two-loop implicit sparse matrix numerical integration (TLISMNI) procedure for the solution of constrained rigid and flexible multibody system differential and algebraic equations is proposed. The proposed method ensures that the kinematic constraint equations are satisfied at the position, velocity and acceleration ...

... PARTIAL DIFFERENTIAL EQUATIONS, NUMERICAL ANALYSIS), (*NUMERICAL ANALYSIS, FOURIER ANALYSIS), (*NUMERICAL ANALYSIS ...