Abstract. The incompatibilities between the initial and boundary data will cause singularities at the time-space corners, which in turn adversely affect the accuracy of the numerical schemes used to compute the solutions. We study the corner singularity issue for nonlinear evolution equations in 1D, and propose two remedy procedures that effectively recover much of the accuracy of the numerical...

1. Jo SH, Youn TJ, Koo BK, et al. Renal toxicity evaluation and comparison between Visipaque (iodixanol) and Hexabrix (ioxaglate) in patients with renal insufficiency undergoing coronary angiography: the RECOVER study: a randomized controlled trial. J Am Coll Cardiol 2006;48:924–30. 2. Jo SH, Youn TJ, Park JS, et al. Iodixanol is less nephrotoxic than ioxaglate in patients with renal insufficie...

Overprecision is the most robust type of overconfidence. We present a new method that significantly reduces this bias and offers insight into its underlying cause. In three experiments, overprecision was significantly reduced by forcing participants to consider all possible outcomes of an event. Each participant was presented with the entire range of possible outcomes divided into intervals, an...