New Step Size Control Algorithm for Semi-Implicit Composition ODE Solvers

Composition is a powerful and simple approach for obtaining numerical integration methods of high accuracy order while preserving the geometric properties basic integrator. Adaptive step size control allows one to significantly increase performance methods. However, there lack efficient algorithms composition solvers due some known difficulties in constructing low-cost embedded local error estimator. In this paper, we propose novel estimator based on difference between semi-implicit CD method semi-explicit midpoint within common scheme. We evaluate adaptive schemes with proposed estimator, comparing it other state-of-the-art approaches. show that ODE algorithm possess higher efficiency than methods, by using comprehensive set nonlinear test problems.