An Accurate Operator Splitting Scheme for Nonlinear

EEcient numerical schemes for nonlinear diiusion l-tering based on additive operator splitting (AOS) were introduced in 15]. AOS schemes are eecient and unconditionally stable, yet their accuracy is low. Future applications of nonlinear diiusion ltering may require additional accuracy at the expense of a relatively modest cost in computations and complexity. To investigate the eeect of higher accuracy schemes, we rst examine the Crank-Nicolson and DuFort-Frankel second-order schemes in one dimension. We then extend the AOS schemes to take advantage of the higher accuracy that is achieved in one dimension, by using symmetric multiplicative splittings. Quantitative comparisons are performed for small and large time steps, as well as visual examination of images to nd out whether the improvement in accuracy is noticeable .