Though computational science is applied in a variety of fields, it is unified by the methods and devices it employs. Many seemingly disparate applications in different fields can be tackled by similar methods.

Some of these methods are:

• The foundation of most computational applications are the methods of applied mathematics, in particular:
  • Linear algebra is a basic set of operations and has entered computer design in the form of vector computers.

  • Differential equations are the primary means of modeling physical processes.

  • Integral equations play an important role in imaging and visualization.

• Methods to deal with large systems come from statistical physics. In particular, it gave rise to stochastic methods and Monte Carlo algorithms that can be used to simulate many real-world processes in such disparate fields as materials science and computational finance.

• High-performance computers are the basic devices used to implement computational solutions. While they classically came as supercomputers based on vector and massively parallel architectures, they have recently been complemented by less expensive cluster computers based on off-the-shelf components.

• Visualization techniques are employed to present the results of computational simulation in a way that can be easily and intuitively understood.

• Discrete mathematics and combinatorial optimization provide computational methods for optimizing real-world processes as well as the mathematical foundations of computer algorithms.