2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/32654ADF95 is a tool to automatically calculate numerical first derivatives for any mathematical expression as a function of user defined independent variables. Accuracy of derivatives is achieved within machine precision. ADF95 may be applied to any FORTRAN 77/90/95 conforming code and requires minimal changes by the user. It provides a new derived data type that holds the value and derivatives and applies forward differencing by overloading all FORTRAN operators and intrinsic functions. An efficient indexing technique leads to a reduced memory usage and a substantially increased performance gain over other available tools with operator overloading. This gain is especially pronounced for sparse systems with large number of independent variables. A wide class of numerical simulations, e.g., those employing implicit solvers, can profit from ADF95.24 pages, 2 figures, 4 tables, accepted in Computer Physics CommunicationsMathematical SoftwareD.1.5; G1.7; G1.8; G.4; J.2text