A new time-domain approach to the derivation of a Jacobi scaled matrix is presented. The Jacobi scaled matrix derived, together with the Jacobi integration matrix, is used to analyse and identify functional differential equations containing terms with a scaled argument. The algorithms proposed are easily implementable on a digital computer. As illustrated in the examples included, the Jacobi method has a faster convergence rate than other types of orthogonal function, such as the Walsh, block-pulse and Laguerre functions.