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In general, high order splitting methods suffer from an order reductionphenomena when applied to the time integration of partial differentialequations with non-periodic boundary conditions. In the last decade, there wereintroduced several modifications to prevent the second order Strang Splittingmethod from such a phenomena. In this article, inspired by these recentcorrector techniques, we introduce a splitting method of order three for aclass of semilinear parabolic problems that avoids order reduction in thecontext of non-periodic boundary conditions. We give a proof for the thirdorder convergence of the method in a simplified linear setting and confirm theresult by numerical experiments. Moreover, we show numerically that the highorder convergence persists for an order four variant of a splitting method, andalso for a nonlinear source term.

Overcoming the order barrier two in splitting methods when applied to semilinear parabolic problems with non-periodic boundary conditions