Harten made fundamental contribution to the development of high-resolution schemes for the solution of hyperbolic partial differential equations.

Among other contributions, he developed the total variation diminishing scheme, which gives an oscillation free solution for flow with shocks.

[2] In 1980s, Harten along with Björn Engquist, Stanley Osher, and Sukumar R. Chakravarthy developed the essentially non-oscillatory (ENO) schemes.

The article on ENO, titled, Uniformly High Order Accurate Essentially Non-oscillatory Schemes, III was published in Journal of Computational Physics, in 1987 [3] and is one of the most cited papers in the field of scientific computing.

[5] In 1990 Harten gave a talk on "Recent developments in shock-capturing schemes" at the International Congress of Mathematicians in Kyoto.