High-performance Method-switching ODE Solver

Computer simulation of systems described by ordinary differential equations imposes a number of requirements to the numerical solvers. One of the most important is a computational efficiency. To evaluate it, usually the maximal error of the numerical solution and the calculation time are used. The most common ways to integrate differential equations are single-step and multistep methods. Single-step integration demonstrates better stability and accuracy. However, such methods slower than multistep counterparts. Thus, both approaches are not optimal according to the mentioned criteria. The hybrid solver that combines the advantages of both integration approaches is seen as prospective. In this article, we consider such solver based on switching between two integrators. The choice of method depends on local error analysis of the obtained numerical solution. Numerical experiments show that such solver is effective for simulation of non-stiff systems described by ordinary differential equations.