Convergence Analysis for Operator Splitting Methods
نویسنده
چکیده
We analyze the order of convergence for operator splitting methods applied to conservation laws with stii source terms. We suppose that the source term q(u) is dissipative. It is proved that the L 1 error introduced by the time-splitting can be bounded by O((tkq(u 0)k L 1 (R)), which is an improvement of the O(Qt) upper bound, where t is the splitting time step, Q is the Lipschitz constant of q or Q = max u jq 0 (u)j in case q is smooth. We also propose a non-uniform temporal mesh which can eliminate the eeect of the initial layer introduced by the stii source term.
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