Implicit for Local Effects and Explicit for Nonlocal Effects Is Unconditionally Stable

@inproceedings{AnitescuImplicitFL,
  title={Implicit for Local Effects and Explicit for Nonlocal Effects Is Unconditionally Stable},
  author={Mihai Anitescu and Faranak Pahlevani and William J. Layton}
}
A combination of implicit and explicit timestepping is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. Loosely speaking, the method we consider is implicit in local and stabilizing terms in the underlying PDE and explicit in nonlocal and unstabilizing terms. Unconditional stability and convergence of the numerical scheme are proved by the energy method and by algebraic techniques. This stability result is… CONTINUE READING

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