Backward differential formulae (BDF) are the basis of the highly efficient schemes for the numerical solution of stiff ordinary differential equations for decades. An alternative multistep scheme (RBDF) based on barycentric rational interpolation is proposed. Specifically, robust new methods of orders 1 to 5 are derived. The local truncation error is analyzed for variable stepsizes in order to implement a variable order, variable stepsize prototype in Matlab. Aspects of the implementation are addressed in detail. Numerical experiments illustrate that the RBDF code compares well with Matlab’s ode15s.

中文翻译：

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非均匀网格上刚性常微分方程的线性重心有理后向微分公式

几十年来，后向微分公式 (BDF) 是刚性常微分方程数值求解高效方案的基础。提出了一种基于重心有理插值的替代多步方案（RBDF）。具体来说，导出了 1 至 5 阶的鲁棒新方法。对可变步长的局部截断误差进行分析，以便在Matlab中实现可变阶数、可变步长原型。详细讨论了实施的各个方面。数值实验表明，RBDF代码与Matlab的ode15s相比效果很好。