Scientific Computing is about contructing mathematical models, adapting numerical solution techniques and using computers to analyse scientific and engineering problems. The field is distinct from computer science which is the study of computers and computations. It is also different from theory and experiment which are the traditional forms of science and engineering. The Scientific Computing approach is to gain understanding, mainly through the analysis of mathematical models implemented on high-performance or super computers.
Numerical analysis is a major technique used in the art of Scientific Computing. Numerical simulations have different objectives depending on the nature of the task being simulated:
- Reconstruct and understand known events (earthquake, tsunamis and other natural disasters)
- Optimise known scenarios (technical and manufacturing processes)
- Predict future or unknown situations (weather, sub-atomic particle behaviour)
Algorithms and mathematical methods used in Scientific Computing include:
- Numerical analysis
- Application of Taylor series as convergent and asymptotic series
- Computing derivatives by finite differences
- High order difference approximations via Taylor series and Richardson extrapolation
- Methods for integration on a uniform mesh: rectangle rule, trapezoid rule, midpoint rule, Simpson's rule
- Runge Kutta method
- Monte Carlo methods
- Numerical Linear Algebra
- Computing the factors by Gauss elimination
- Choleski factorizations
- Discrete Fourier transform and applications.
- Newton's method
- Time stepping methods for dynamical systems
The term computational scientist is used to describe someone skilled in the arts of Scientific Computing. This person is usually a scientist, an engineer or an applied mathematician who applies high-performance computers in different ways to advance the state-of-the-art in their respective applied disciplines in physics, chemistry and engineering. Scientific Computing has also begun to make an influence on other areas such as economics, biology and medicine.
Programming languages used for Scientific Computing applications include Fortran, APL, MATLAB, Mathematica and the J programming language.
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