In this work we construct a multiderivative implicit-explicit (IMEX) scheme for a class of stiff ordinary differential equations. Our solver is high-order accurate and has an asymptotic preserving (AP) property. The proposed method is based upon a two-derivative backward Taylor series base solver, which we show has an AP property. Higher order accuracies are found by iterating the result over a high-order multiderivative interpolant of the right hand side function, which we again prove has an AP property. Theoretical results showcasing the asymptotic consistency as well as the high-order accuracy of the solver are presented. In addition, an extension of the solver to an arbitrarily split right hand side function is also offered. Numerical results for a collection of standard test cases from the literature are presented that support the theoretical findings of the paper.

中文翻译：

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渐近保持半隐式多导数求解器

在这项工作中，我们为一类刚性常微分方程构建了一个多导隐式显式 (IMEX) 方案。我们的求解器是高阶准确的，并且具有渐近保持 (AP) 属性。所提出的方法基于二阶逆向泰勒级数基求解器，我们展示了它具有 AP 属性。通过在右侧函数的高阶多导数插值上迭代结果，可以找到更高阶的精度，我们再次证明它具有 AP 属性。理论结果显示了渐近一致性以及求解器的高阶精度。此外，还提供了对任意拆分右侧功能的求解器的扩展。