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In this paper, we investigate two-step Runge–Kutta methods to solve Volterra integro-differential equations. Two-step Runge–Kutta methods increase the order of convergence in comparing the classical Runge–Kutta method without extra computational cost. First, the local order conditions and convergence theorem are derived. Then, stability properties of two-step Runge–Kutta methods corresponding to the basic and convolution test equations are analysed. Furthermore, one-stage method with order four and two-stage method with order six are constructed and we plot the stability regions. Numerical examples are presented to confirm the theoretical analyses. [ABSTRACT FROM AUTHOR]

This paper investigates the relationship between business strategy and sustainability of Chinese SMEs and how the environmental uncertainty may affect this relationship. It analyses the impact of active and passive business strategies on firms' sustainability and tests the potential moderating role of economic policy uncertainty in this relationship. The empirical analysis is performed by employing fixed-effect and GMM estimations on data collected from 937 Chinese A-share non-financial companies listed on the Shanghai and Shenzhen stock exchanges from 2010 to 2021. The results show that the high-risk active business strategy of innovation and new market development is associated with greater business sustainability, and this relationship is stronger for SMEs than for non-SMEs in China. Moreover, higher economic policy uncertainty strengthens the positive relationship between active business strategy and firm sustainability, implying that in periods of higher environmental uncertainty firms which pursue active business strategy achieve greater business sustainability. These findings are useful for devising business strategy and can assist in formulating policy initiatives seeking to ensure sustainable development of SMEs in China. [ABSTRACT FROM AUTHOR]