A Method for the Spatial Discretization of Parabolic Equations in One Space Variable

This paper is concerned with the design of a spatial discretization method for polar and nonpolar parabolic equations in one space variable. A new spatial discretization method suitable for use in a library program is derived. The relationship to other methods is explored. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithm and to compare it with other recent codes. 1. Introduction. The aim of this paper is to describe and to give evidence in support of a new spatial discretization for the method of lines solution of parabolic equations in one space variable. The intent is to provide a method that is suitable for use in a general-purpose library program, such as the D03P section of the NAG library. Ordinary and parabolic partial differential equations in one space variable x often