Shi, Jian2005-11-232005-11-231992http://hdl.handle.net/1826/188This report investigates the general theory and methodology of high resolution numerical schemes for one-dimensional hyperbolic conservation laws. The Universal Formula from which 2-level explicit conservative arbitrary-order numerical methods can be derived is developed. This report also explores the issue of linear stability. A new approach to linear stability analysis is presented. The generalized formulation for TVD methods with stable region of -1 ≤ c ≤ 1 proposed. To demonstrate the theories, some third order and fourth order TVD methods are generated.1963 bytes2006696 bytestext/plainapplication/pdfen-UKTechnical Report