our results using the Fast Fourier Transformation, the N-body attraction problem, and the cubic splines interpolation as examples.We investigate the application of partial evaluation to numerically oriented computation in scientific and engineering applications. We present our results using the Fast Fourier Transformation, the N-body attraction problem, and the cubic splines interpolation as examples. All programs are written in Fortran 77, specialized using our Fortran partial evaluator, and compiled into executable machine code using a commercial Fortran compiler. The results demonstrate that existing partial evaluation technology is strong enough to improve the efficiency of a large class of numerical programs. However, using partial evaluation as a development tool in the `real world' still remains a challenging problem. Our work differs from most previous works in that we apply partial evaluation in a more realistic setting. We use Fortran that, after all, is the most widely ...