The application of generalized, cyclic, and modified numerical integration algorithms to problems of satellite orbit computation

Generalized, cyclic, and modified multistep numerical integration methods are developed and evaluated for application to problems of satellite orbit computation. Generalized methods are compared with the presently utilized Cowell methods; new cyclic methods are developed for special second-order differential equations; and several modified methods are developed and applied to orbit computation problems. Special computer programs were written to generate coefficients for these methods, and subroutines were written which allow use of these methods with NASA's GEOSTAR computer program

Numerical analysis of some integral equations with singularities

In this thesis we consider new approaches to the numerical solution of a class of Volterra integral equations, which contain a kernel with singularity of non-standard type. The kernel is singular in both arguments at the origin, resulting in multiple solutions, one of which is differentiable at the origin. We consider numerical methods to approximate any of the (infinitely many) solutions of the equation. We go on to show that the use of product integration over a short primary interval, combined with the careful use of extrapolation to improve the order, may be linked to any suitable standard method away from the origin. The resulting split-interval algorithm is shown to be reliable and flexible, capable of achieving good accuracy, with convergence to the one particular smooth solution.Supported by a college bursary from the University of Chester

Numerical analysis of some integral equations with singularities

In this thesis we consider new approaches to the numerical solution of a class of Volterra integral equations, which contain a kernel with singularity of non-standard type. The kernel is singular in both arguments at the origin, resulting in multiple solutions, one of which is differentiable at the origin. We consider numerical methods to approximate any of the (infinitely many) solutions of the equation. We go on to show that the use of product integration over a short primary interval, combined with the careful use of extrapolation to improve the order, may be linked to any suitable standard method away from the origin. The resulting split-interval algorithm is shown to be reliable and flexible, capable of achieving good accuracy, with convergence to the one particular smooth solution.EThOS - Electronic Theses Online ServiceUniversity of ChesterGBUnited Kingdo

SciCADE 95: International conference on scientific computation and differential equations

This report consists of abstracts from the conference. Topics include algorithms, computer codes, and numerical solutions for differential equations. Linear and nonlinear as well as boundary-value and initial-value problems are covered. Various applications of these problems are also included

Numerical solution of three-dimensional incompressible unsteady viscous flows

Issued as Semi-annual progress reports [nos. 1-7], and Final report, Project E-16-61

The determination of non-stationary random vibration response characteristics by numerical simulation techniques

The technique of sample averaging is considered for application to the non-stationary vibration problem associated with road vehicle ride. Time history realisations of the vehicle response are achieved by a discretised Iumped parameter model idealisation simulated on a digital computer. Sets of realisation histories are collated to obtain the overal statistical response characteristics. The road vehicle ride problem is the result of random road roughness exciting the vehicle as it traverses the surface. This dynamic excitation may be considered as a stationary function of time, provided the vehicle traverse velocity does not vary. Under variable velocity conditions the excitation is a non-stationary function of time. It is the solution of this non-stationary accelerating vehicle problem which is the subject of this study. An alternative method of solution for the non-stationary vehicle problem has already been achieved. This alternative, like sample averaging, places heavy emphasis on the use of numerical methods on a digital computer for the evaluation of results. Unlike sample averaging, it is not normally applicable to road vehicles which possess significant non-linear dynamic characteristics in their suspension configuration. Ultimately the objective of this thesis is to make a comparative appraisal of the viability of sample averaging as a general means of determining the non-stationary response characteristics of road vehicles. To permit full justification of the technique and thereby ensure flexibility of application, it is imperative that all methods of digital simulation are scrutinised prior to implementation. In essence the simulator consists of two distinct numerical modules. One module is concerned with the generation of a large sample of statistically independent road surface profile realisations, while the other applies itself to analysing vehicle response. The additional problems encountered when interfacing the two modules are also fully investigated. Upon implementation, the simulator proves itself a flexible and viable tool for the solution of the non-stationary problem while providing some surprisingly new observations

Numerical Boundary Condition Procedures

Topics include numerical procedures for treating inflow and outflow boundaries, steady and unsteady discontinuous surfaces, far field boundaries, and multiblock grids. In addition, the effects of numerical boundary approximations on stability, accuracy, and convergence rate of the numerical solution are discussed