In a previous paper, a technique was suggested to avoid order reduction with any explicit exponential Runge-Kutta method when integrating initial boundary value nonlinear problems with time-dependent boundary conditions. In this paper, we significantly simplify the full discretization formulas to be applied under conditions which are nearly always satisfied in practice. Not only a simpler linear combination of $\varphi_j$-functions is given for both the stages and the solution, but also the information required on the boundary is so much simplified that, in order to get local order three, it is no longer necessary to resort to numerical differentiation in space. The technique is then shown to be computationally competitive against other widely used methods with high enough stiff order through the standard method of lines.

翻译：在先前的一篇论文中，我们提出了一种技术，旨在当求解含时变边界条件的初边值非线性问题时，避免任何显式指数龙格-库塔方法中出现阶降现象。本文中，我们大幅简化了在近乎实际条件下适用的全离散化公式。不仅针对中间阶段和解给出了更简单的 $\varphi_j$ 函数线性组合，边界所需信息也得到极大简化，以至于在获取三阶局部精度时，不再需要依赖空间上的数值微分。通过标准线方法，该技术在计算效率上展现出与具有足够高刚性阶的广泛使用方法的竞争力。