High-order splitting methods for separable non-autonomous parabolic equations

Higher-order operator splitting methods for deterministic parabolic equations

University of Cambridge Splitting Methods for Non-autonomous Diierential Equations Splitting Methods for Non-autonomous Diierential Equations

A new fourth order splitting method is presented which in a certain measure is optimal. In combination with a new way of handling non-autonomous problems, the schemes we present are based on Mag-nus expansions and they show very promising results when applied to Hamiltonian ODEs.

Optimized high-order splitting methods for some classes of parabolic equations

We are concerned with the numerical solution obtained by splitting methods of certain parabolic partial differential equations. Splitting schemes of order higher than two with real coefficients necessarily involve negative coefficients. It has been demonstrated that this second-order barrier can be overcome by using splitting methods with complex-valued coefficients (with positive real parts). ...

[hal-00759579, v1] Optimized high-order splitting methods for some classes of parabolic equations

We are concerned with the numerical solution obtained by splitting methods of certain parabolic partial differential equations. Splitting schemes of order higher than two with real coefficients necessarily involve negative coefficients. It has been demonstrated that this second-order barrier can be overcome by using splitting methods with complex-valued coefficients (with positive real parts). ...

Splitting methods for non-autonomous linear systems

We present splitting methods for numerically solving a certain class of explicitly time-dependent linear differential equations. Starting from an efficient method for the autonomous case and making use of the formal solution obtained with the Magnus expansion, we show how to get the order conditions for the non-autonomous case. We also build a family of sixth-order integrators whose performance...