In the process of changes in total population, structure, and spatial distribution, it is essential to investigate the inner rules of the harmonious correlation between population and development. Thus, this study examines the correlation between demographic variables (e.g., delayed retirement, total fertility rate, and life expectancy) and economic development in China based on the overlapping generations (OLG) model and numerical simulation method. The findings reveal the following: (1) total social output level positively correlates with survival probability; (2) the contribution of the aging labor force (retirement age delay) to the total output is significant and an essential source of sustainable economic growth; (3) aggregate output increases first and then decreases with the increase in individual pension contributions rate, and the correlation between the two is a ∩-shaped curve. The policy implications of this study are that China’s economic transformation is a general trend, which should promote the upgrading of the demographic dividend from quantitative type to qualitative type and tap the human capital potential to increase the capital-based demographic dividend and activate the gender dividend.

In this paper, a new explicit fourth-order Runge–Kutta method adapted to oscillatory problems with two frequencies (μ and ν) is developed. The new method can integrate exactly the different harmonic oscillators $y^{\prime }=\mathrm{i}\mu y$ and $y^{\prime }=\mathrm{i}\nu y$ simultaneously. Numerical stability and phase properties of the new method are analysed. Numerical experiments are conducted to illustrate the high accuracy and competence of our new method in comparison with some highly effective methods from the recent literature.