Numerical verification method on complex ODEs for existence of global solutions within finite domains

抄録

A numerical verification method is proposed to prove the existence of time-global solutions of complex ordinary differential equations (ODEs), which should be inscribed within a circle with a specified radius r. A conservative quantity is assumed to exist and is calculated to construct the verification conditions. We use a numerical example with a series expansion on the right side of the ODEs to demonstrate how to find such a conservative quantity and how to apply our method.