Handling effectively the rejected stages in Runge–Kutta pairs implementation
Er‐Ping Xiang,
Chia‐Liang Lin,
T. E. Simos
et al.
Abstract:Runge–Kutta (RK) pairs are widely used for numerically solving initial value problems (IVPs), but dealing with step rejections during integration is a common occurrence. Conventionally, when a step is rejected, all calculations made during that step are discarded, and a completely new set of computations is initiated. In our research, we propose a method to address this inefficiency by repurposing the previously computed RK stages from rejected steps. Our primary focus is on the renowned RKF45 pair, consisting… Show more
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