Stable predictor-corrector methods for first order ordinary differential equations

Because of the wide variety of differential equations, there seems to be no numerical method which will affect the solution best for all problems. Predictor-corrector methods have been developed which utilize more ordinates in the predictor and corrector equations in the search for a better method. These methods are compared for stability and convergence with the well known methods of Milne, Adams, and Hamming --Abstract, page ii

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