Department of Applied Mathematics,

Dalian University of Technology,

Dalian 116023,

P.R. CHINA

E-mail: zhanghq@dlut.edu.cn

**The arithmetic model in mechanization of mathematical
physics**

**Abstract:**

Mechanization of mathematical physics consists of two parts: mechanized
solveing system and mechanized reasoning system in mathematical physics.
In this talk we try to construct these systems with an united
theory. For this purpose, we introduce the concepts of C-D pairs, C-D intetrable
system and A-C net respectively. There are several algorithms to construct
C-D pairs and A-C net respectively. AC=BD model plays an important role
for finding these algorithms. In the machanized solveing system, we construct
lots of analytic solutions for various kinds of differential equations,
especially for nonlinear differential equations.