科研成果详情

We analyze the order of convergence for operator splitting methods applied to conservation laws with stiff source terms. We suppose that the source term q(u) is dissipative. It is proved that the L1 error introduced by the time splitting can be bounded by O(δt∥q(u0)∥L1), which is an improvement of the O(Qδt) upper bound, where δt is the splitting time step, Q is the Lipschitz constant of q, or Q = maxu |q′(u)| in case q is smooth. A generic model with a special form of stiff source is also investigated. We propose a nonuniform temporal mesh to eliminate the effect of the initial layer introduced by the stiff source term. Our results are derived by using parabolic regularizations, rather than using Kuznetsov's approximation theory, which has been employed as a standard approach for error analysis to the dimensional- or time-splitting methods. Numerical examples are presented to illustrate the theoretical results.