Philosophers and historians of science have only recently begun to think about issues involving the use of computer simulations in scientific practice. This dissertation is meant to help develop a more broadly construed philosophy and history of computer simulation than has previously been presented by considering terminological, epistemological, and ontological questions as they bear on the question of scientific methodology in regard to computer simulation from a historical perspective. One common argument that has emerged in the literature is that computer simulations cannot count as experiments because (1) empirical theory testing cannot be performed with a computer simulation since it must assume the very theory that is supposedly being tested and (2) empirical theory testing is the only form of theory guided experimentation. While there is lively discussion about the veracity of (1), the extant literature in both the philosophy and history of computer simulation and experimentation tacitly assumes (2). This dissertation undermines (2) by introducing a new experimental genre – the "Kuhnian" experiment. Kuhnian experiments do not test theory, but rather assume the adequacy of some scientific theory in order to solve empirical puzzles in scientific fields where the theory is already well articulated and fully accepted. Such puzzles arise as a result of the theoretical equations describing the physical phenomenon in question being analytically intractable. One way scientists solve these puzzles is through computer simulation. Historical case studies are presented as examples of this sort of experimental puzzle solving for two types of computing technology: analog computers (the network analyzer) and digital computers (particle diffusion using the Monte Carlo method). This is underexplored territory in the history of science, and thus this dissertation serves to augment the historical understanding of computational science.