The power and availability of modern computers have made numerical calculations, computer simulations and other use of high performance computers to an important tool in almost all disciplines of science and engineering. Many researchers claim that computing has become a third main method for doing investigations, besides theory and experiments. Computing may be used insted of theory and experiments by providing insight in many phenomena that are too complex to be handled by analytical methods, too expensive, too dangerous or impossible to study through experiments. computing may also be asupplement to theory and experimentation resulting in an interplay among the three main methods.

A very short ( informal) definition of computational  science is given by D.E. Stevenson in his article Science Computational scince and Computer Science: At a Crossroads:

"We describe computational science as an interdisciplinary approach to doing scicne on computers."

Golub and Ortega give the following working definition of "scientific computing":

"Scientific computing is the collection of tools, techniques, and theories required to solve on a computer mathematical models of problems in science and engineering."

Gloub and Ortega describe the difference in the following way:

"... The technique used to obtain such solutions [of mathematical models that represent some physical situation] are part of the general area called scientific computing, and the use of these techniques to elicit insight into scientific or engineering problems is called computational science ( or computeational engineering)."

The difference expressed in the second part of this quotation may become a bit clearer when another difinition is considered.

"... use of HPC technology to advance the state of knowledge in a particular applications discipline"