The development of tourism promotes the rapid development of regional economy. Balancing the relationship between investment and income of tourism is important, which affects the speed of economic development. Based on the background of tourism economy, to a specific mode of regional tourism, the first step is to collect information, for the coupling analysis between the subsystems of the tourism industry and regional economy of synergy, through the tourism development index of income differential mathematical equations of finite element calculation, a mathematical model built for the tourism income. By solving the finite element ordinary differential mathematical equation, the relationship between tourism maximum income, effective income and investment cost is obtained. Finally, the stability of the mathematical model is analysed. This study evaluates and predicts the income index of tourism development in a specific region and provides countermeasures for the development of tourism economy in this region.