Second-order, L0-stable methods for the heat equation with time-dependent boundary conditions

A family of second-order, Lo-stable methods is developed and analysed for the numerical solution of the simple heat equation with time-dependent boundary conditions. Methods of the family need only real arithmetic in their implementation. In a series of numerical experiments no oscillations, which are a feature of some results obtained using Ao-stable methods, are observed in the computed solutions. Splitting techniques for firstand secondorder hyperbolic problems are also considered.