On the Convergence Rate ofOperator Splitting for Hamilton-Jacobi Equations with Source Terms

We establish a rate of convergence for a semi-discrete operator splitting method applied to Hamilton-Jacobi equations with source terms. The method is based on sequentially solving a Hamilton-Jacobi equation and an ordinary diierential equation. The Hamilton-Jacobi equation is solved exactly while the ordinary diierential equation is solved exactly or by an explicit Euler method. We prove that the L 1 error associated with the operator splitting method is bounded by O((t), where t is the splitting (or time) step. This error bound is an improvement over the existing O(p t) bound due to Souganidis 40]. In the one dimensional case, we present a fully discrete splitting method based on an unconditionally stable front tracking method for homogeneousHamilton-Jacobiequations. It is proved that this fully discrete splitting method possesses a linear convergence rate. Moreover, numerical results are presented to illustrate the theoretical convergence results.