中文摘要：

基于凹凸分离的思想,对一类常微分方程提出了新的一阶和两阶数值格式.在经典BDF格式的基础上,对能量函数中的凹项部分进行显式处理或者外推处理,得到了新的计算数值格式,并给出了稳定性和收敛性分析.同时格式被应用到Allen-Cahn方程,数值例子表明格式是有效的.

英文摘要：

Two new schemes of first-order and second-order are proposed for some ordinary differential equations,with the idea of convex splitting.Based on classical BDF scheme,the new schemes are constructed by applying explicit or extrapolating approach to the concave part in energy function.Stability and convergence analysis are also established.Meanwhile,the new schemes are used to solve Allen-Cahn equations,and are verified to be efficient by numerical examples.