In this paper we consider various multi-component splittings based on the trapezoidal rule and the implicit midpoint rule. It will be shown that an important requirement on such methods is internal stability. The methods will be applied to initial-boundary-value problems. Along with a theoretical analysis, some numerical test results will be presented.

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Department of Numerical Mathematics [NM]
Discretization of evoluation problems

Hundsdorfer, W. (1996). Trapezoidal and midpoint splittings for initial-boundary value problems. Department of Numerical Mathematics [NM]. CWI.