A. V. BOBYLEV and T. OHWADA
On the generalization of Strang's splitting scheme
Received: 27 September 1999
Mathematics Subject Classification (2000): 65G99 - 76P05
Abstract The accuracy of splitting method is investigated in an abstract Cauchy problem and is shown to be first order in time for general evolutionary equations except for a special case. A general formula for the leading term is obtained. It is also shown as an immediate consequence of the formula that the accuracy is improved from first order to second order by a simple modification. Such a modification was first proposed by Strang [G. Strang, SIAM J. Numer. Anal. 5 (1968), 506-517] for PDEs. Thus, the Strang result is generalized in the present paper to the case of arbitrary evolutionary equations. In particular, it is valid for practically important case of integro-differential nonlinear kinetic equations and therefore there is no need to make additional error estimations in each particular case. The accuracy of generalized Strang's splitting method is demonstrated numerically for the BGK equation.