Nonlinear ordinary differential equations with discontinuities

Differential Equations with discontinuous right hand sides often do not have classical solutions. In particular, differential equations which contain a signum function are investigated. The Filippov definition of a solution is introduced and a numerical method is established for approximating a Filippov solution for these differential equations. The signum is then approximated by a continuous function whose limiting function is the signum function and a numerical method is established for approximating a solution using the continuous function.