Bipenalty Method for Stable Time Integration Algorithms in Computational Physics

In many areas of engineering and science, computer simulations are used for analysis and design. If the time dimension is relevant, time integration algorithms become an important ingredient of the numerical simulation software. The most popular time integrator is the so-called "explicit time integration" algorithm, which is simple to formulate and straightforward to implement. The main drawback of explicit time integration is its conditional stability: the time increment must be chosen smaller than a certain critical time increment, otherwise the numerical simulation becomes unstable.