Adaptive explicit-implicit switching solver for stiff ODEs

摘要

Computer simulation of stiff dynamical systems usually requires researchers and engineers to apply implicit numerical quadrature formulae. The most efficient of stiff ODE solvers use adaptive timestep technique, which reduces computational costs by varying integration step size according to the local truncation error estimation. Due to their stability, the implicit methods can handle large step sizes in “slow” solution segments and thus speed up computations. However, in “fast” solution segments, small integration steps are still needed to meet the accuracy requirements. These small steps can be calculated via explicit integration method without loss of the solution stability for many practical problems. This adaptive method switching technique allows reducing computational costs while solving stiff ODEs. In this paper, variable time step and numerical quadrature formula ODE solver is proposed. Numerical tests show its superior performance, up to ten times higher than traditional solvers performance.