Aspects of Realization

Discontinuities may not only appear in the right hand side function and in the solution but also in the system s Jacobian. They must be taken into consideration if Newton iteration is used to solve nonlinear systems in the course of an implicit discretization method or in steady state computation. Different impacts of a discontinuity must be handled  

Each of these discontinuities require different actions with respect to convergence control (a), recomputation and decomposition of the Jacobian (b) or even reinitialization of the simulation model (c). 

Switching functions should be as simple as possible, e.g. linear. It is advisable to use different switching functions for different discontinuities instead of multiplying them to obtain only one function. 

7 Other Methods and Codes for Discontinuous Differential Equations 

There are some articles proposing methods for localizing discontinuities by monitoring the error estimation, which grows significantly if a discontinuity is crossed 

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However, practical aspects of realization of these ideas in the optical diapason are not solved yet. 

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