[1] – 

The eclipse maps presented on this website were computed using EclipseSimulator.

This is an open-source tool which traces the positions of the Sun, Earth and Moon over the course of each eclipse and traces the path of the Moon's shadow across the Earth's surface. It was written by the author and freely available for download from GitHub.

EclipseSimulator takes the positions of each body from the JPL DE430 planetary ephemeris. It treats the Earth and Moon as ellipsoids with the same polar and equatorial radii which are also assumed by Fred Espenak's eclipse predictions. All eclipse predictions are made at sea level. The predictions here match those calculated by Xavier Jubier to within a few kilometers.

[2] – 

Espanak, F., & Meeus, J., Five Millennium Canon of Solar Eclipses: -1999 to +3000, NASA Technical Publication TP-2006-214141 (2006)