“Computational science (also scientific computing or
scientific computation) is concerned with constructing mathematical models and
quantitative analysis techniques and using computers to analyze and solve
scientific problems.” (Wiki) Natural scientific laws are commonly expressed by various
types of mathematical equations. The purpose of scientific computing is to find
numerical solutions of these equations. This kind of calculation involves a
huge amount of computations. Simple calculation tools cannot achieve this goal.
Before the appearance of computers, scientific researches and engineering designs
mainly rely on the data from experiments or tests and computing is only used
for assistance. Because of the rapid development of computers, more and more
complex calculations become possible. Utilizing the computer for scientific
computing has brought huge economic benefits as well as made scientific technology
itself fundamental change—the traditional scientific technology only includes two
components: theory and experiment. Computing has become the third component
that as important as the other components after using computers.
Computing process includes three stages: the establishment of mathematical
model, the establishment of solving computational methods, and computer
implement.
To establish a mathematical model is establish a series of quantitative
relations for investigative objects based on the related theories, namely a set
of mathematical formulas or equations. Reasonable to simplify complex models is
an important measure to avoid the excessive computing. Mathematical models
generally contain continuous variables, such as differential equations,
integral equations. They cannot be directly processed on a digital computer. To
this end, the first thing to do is discrete the problem, namely change the
problem into a finite number of unknowns discrete form, such as finite
algebraic equations. Then look for solving methods. Computer implement has a
series of steps, which includes programming, commissioning, operation, and analyzing
results. Development of software technology provides suitable programming languages
and other software tools for scientific computing that greatly improve efficiency
and reliability.
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