This paper presents the Alternating Segment Explicit-Implicit (ASE-I) method forsolving the convection-diffusion equation. The method has the obvious property ofparallelism, and is unconditionally stable. Numerical example is presented.
The algebraic expressions describing the geometric properties of mesh curves aregiven. The control functions concering above properties are introduced and functionalsshowing those properties are constructed. Based on a theorem, we get the concretecorresponding relation of the control functions with the mesh properties when thefuctional taken minimum. By the numerical solution of Euler equation obtained fromfunctional minimum, we get the needed grids. This method of grids generation has aquit derict geometric meaning, and its inner control is flexible. Particularly not onlythe adaptability with physical preoblem is concerned, but also the adaptability with thereal physical region. The numerical experiments verified the efficiency of our method.
