Consistency and convergence of SPH approximations

Includes bibliographical references (leaves 58-59).Includes abstract.This thesis is about a new approach to SPH. Instead of using a single kernel or shape function for approximation of a function and its derivatives, individual shape functions are used for each derivative. The investigation is carried out in one space dimension. After producing the conditions for consistency and convergence for the zeroth, first and second derivatives, a new set of linear or piecewise-linear shape functions which meet the minimum of these requirements are presented for each