On Finite Difference Methods of Solution of the Transport Equation

in one form or another, where V is the velocity of propagation of a profile given initially along the .r-axis. Most of these schemes can be found in Richtmyer [1] and, generally speaking, they are chosen primarily from the point of view of stability. An equation of the type (1) has a single family of characteristics in the (x, t) plane and in any step-by-step method of solution it is essential from the point of view of accuracy that the characteristics be followed as closely as possible. It is proposed to examine existing difference schemes from this standpoint and to derive new formulas of greater accuracy. For the purposes of this paper, it is sufficient to consider the simplified version of (1)