论文标题
渐近保存半径的多动求解器
An asymptotic preserving semi-implicit multiderivative solver
论文作者
论文摘要
在这项工作中，我们为一类僵硬的普通微分方程构建了多个隐式解释（IMEX）方案。我们的求解器是高阶准确的，并且具有渐近保存（AP）属性。所提出的方法基于两个衍生的向后泰勒级数基本求解器，我们显示的具有AP属性。通过在右手侧函数的高阶多插入术上迭代结果，可以找到高阶精度，我们再次证明具有AP属性。提出了渐近一致性以及求解器的高阶精度的理论结果。此外，还提供了求解器任意分开的右侧侧函数的扩展。提供了从文献中收集的标准测试用例的数值结果，以支持论文的理论发现。
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.
