On the convergence and local splitting error of different splitting schemes
István Faragó, Ágnes Havasi · Progress in Computational Fluid Dynamics An International Journal · 2005
The convergence of different splitting methods – sequential, Strang, weighted sequential and weighted Strang splitting – is investigated in the semigroup context both for linear and m-dissipative operators, by use of the Trotter product formula and Lax's equivalence theorem. The local splitting errors of the Strang and weighted Strang schemes are analysed with the help of the Baker-Campbell-Hausdorff formula. It is shown that both methods, generally of second order, can be higher than second-order accurate if certain conditions are met. Our results are illustrated with examples.