A very important part of archaeology is to determine the shape of ancient degraded inscriptions and signs with the goal to identify them. The degradation of archaeological signs or hieroglyphs can be simulated by two approaches: backward or forward time integration of the governing equation. In this work, the two-dimensional transient convection-diffusion equation is used with the upper surface height of hieroglyphs as unknown function. This inverse problem is numerically solved by applying forward time integration schemes and the dual reciprocity boundary element method (DRBEM), which allows easy incorporation of different boundary geometries. After designing and implementing a DRBEM degradation model, its calibration is described based on a well-defined hieroglyphic sign still visible in the degraded inscription. Then the calibrated model is applied to identify Hittite hieroglyphs not recognized yet by purely optical techniques. The results gained so far indicate that strongly degraded signs can be recovered to a certain extent and matched to signs in the existing Hittite alphabet.