Stability Test for Periodic Differential Equations on Digital Computers with Applications

Stability Test for Periodic Differential Equations on Digital Computers with Applications. For linear and nonlinear ordinary initial value problems with periodic coefficient functions, a sufficient enclosure test is derived. The successful execution on digital computers guarantees the stability of all solutions in the linear case or the boundedness of all perturbed solutions starting in an admitted finite neighborhood of the initial data in the nonlinear case. Presented applications are concerned with vibrations of gear drives. An implementation of the test using FORTRAN and ACRITH is discussed.