Extrapolation Semi-implicit ODE solvers with adaptive timestep

摘要

Semi-implicit numerical integration methods are an effective trade-off between weakly stable explicit and computationally expensive implicit ODE solvers. Variable stepsize is a proven technique to raise the effectiveness of ODE solvers in real applications. This paper considers the implementation of extrapolation semi-implicit methods with adaptive timestep for a two initial value problems, HIRES and Rössler systems. The performance of various adaptive extrapolation methods was compared by plotting computational costs via truncation error. The study shows the superior performance of semi-implicit extrapolation solvers with adaptive stepsize control applied.