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具有高阶精度并且稳定的显格式在高效求解微分方程中具有重要意义.本文提出一个系统的框架以牺牲部分精度换取稳定性,尤其是可以无条件地保持强稳定性、正性、解的有界性以及收缩性.整个算法框架通过三步构建:(1)引入连续系统的稳定化形式?(2)使用显式指数型方法求积?(3)对指数函数进行合理逼近.在此框架下,通过选取合适的稳定化参数,我们首先展示一类一阶和二阶指数时间差分格式可以无条件保持这些结构,而后将积分因子变换与高阶Runge-Kutta方法以及多步法相结合,开发三种可以无条件保结构的逼近技术:(1)泰勒多项式逼近?(2)递推逼近?(3)指数函数和线性函数的组合逼近.当处理刚性问题时,本文开发的一系列参数化方法可以通过将线性刚性项作为一个积分因子直接应用于这一类问题中.参数化时间积分方法不仅保持了底层格式的显性以及收敛阶,还可以无条件保持相应的结构.使用第二、第三种逼近技术的框架对底层格式的要求相对宽松,仅要求所有的系数非负.因此,参数化Runge-Kutta方法最高可以达到四阶,参数化多步法由于没有阶障碍可以达到任意高阶.本框架中所需的唯一自由参数,即稳定化参数,可以事先由问题所满足的向前Euler条件确定.与隐格式不同的是,文中提出的方法可以在保持稳定的前提下显式求解非线性问题.作为传统条件保结构方法的替代,本方法可以高效求解刚性和非线性问题.针对具有不同刚性项的基准算例测试验证了参数化方法的优越性.“,”High-order accurate and stable explicit methods are powerful in solving differential equations efficiently. In this work, we propose a systematic framework to trade off accuracy for stability, especially the unconditional preservation of strong stability, positivity, range boundedness and contractivity. The whole algorithm consists of three steps: (1) Introducing a stabilizing term in the continuous system?(2) Integrating the system using an explicit exponential method? (3) Substituting the exponential functions with suitable approximations. We first show that a class of first-and second-order exponential time difference Runge-Kutta schemes are capable to preserve structures unconditionally when suitable stabilization parameter is chosen. Then by adopting the integrating factor approach with high-order Runge-Kutta and multi-step schemes as underlying schemes, three different approximation techniques are developed to make high-order schemes unconditionally structure-preserving, i.e., (1) a Taylor polynomial approximation? (2) a recursive approximation? (3) an approximation using combinations of exponential and linear functions. The proposed parametric schemes can be deployed to stiff problems straightforwardly by treating the stiff linear term as an integrating factor. The resulting time integration methods retain the explicitness and convergence orders of underlying time-marching schemes, yet with unconditional preservation of structures. The proposed framework using the second and third approximations has relatively mild requirement on underlying schemes, i.e., all coefficients are non-negative. Thus the parametric Runge-Kutta schemes can reach up to the fourth-order, and there is no order barrier in parametric multi-step schemes. The only free parameter-the stablization parameter in the framework can be determined a priori based on the forward Euler conditions. Unlike implicit methods, the parametric methodology allows for solving nonlinear problems stably and explicitly. As an alternative to conditionally structure-preserving methods, the proposed schemes are promising for the efficient computation of stiff and nonlinear problems. Numerical tests on benchmark problems with different stiffness are carried out to assess the performance of parametric methods.