Calculation of tourism development income index based on finite element ordinary differential mathematical equation

China's tourism industry developed rapidly in the late 1990s, and its direct result is the continuous and rapid growth of tourism operating income. However, since 2010, China's tourism development has been slow and regional tourism development has been uneven. Even in different years in the same area, the tourism operating income shows great differences. How to select the key factor from many factors, as there is still no recognised method in the theoretical circle. This article combines the theories of econometrics, differential calculus, statistics and other related fields. Through in-depth basic research, the data required for the research is determined, and such data are substituted into the self-constructed econometric differential statistical model. Effective analysis of empirical objects is realised. At the same time, the article uses tourism operating income as an indicator and uses the analysis of variance method to calculate the average coefficient of variation of the same region in different years and different regions in the same year, analyses the trends and characteristics of China's tourism in the temporal and spatial structure, and proposes corresponding results on this basis.