Abstract
In this paper, we study the error of a second order finite difference scheme for the one-dimensional convection-diffusion equation. We consider nonsmooth initial conditions commonly encountered in financial pricing applications. For these initial conditions, we establish the explicit expression of the quantization error, which is loosely defined as the error of the numerical solution due to the placement of the point of nonsmoothness on the numerical grid. Based on our analysis, we study the issue of optimal placement of such nonsmoothness points on the grid, and the effect of smoothing operators on quantization errors.
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