In fluid mechanics, how to solve multiple solutions in ordinary differential equations is always a concerned and difficult problem. An improved RNA genetic algorithm inspired by RNA molecular structure and operators is proposed for solving the parameter estimation problems of the multiple solutions that described as the flow of the fluid through a porous channel with expanding or contracting walls. In this paper, multiple solutions can be found through changing accuracy and search coverage and multi-iterations of computer. At last, the ordinary differential equations is calculated, and the result has great accuracy and this method is practical. (C) 2017 The Authors. Published by Elsevier Ltd.