Abstract: For the purpose of overcoming the difficulty of the so-called “intermediateexpression swell” in applying computer algebra, a semi-inverse algorithm is proposed.The order of seeking solutions for various problems is partly inverted, i. e., theintermediate expressions appearing in conrputation are frozen in the symbolic format first, and “unfrozen ”till the formal expressions of final solulions are found out. Inthis way the overflow due to the shortage of saving space is avoided. The applicationsof the algorithm in the problems on nonllinear oscillation. dynamical optimization andinterfacial solilary waves are described. which show the effectiveness of the semi-inverse algorithm.

Key words: computer algebra, symbolic computation, intermediate cxpression swell, perturbation method, nonlinear analysis