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The difference between SCIENTIFIC COMPUTING and COMPUTATIONAL MATHEMATICS
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Scientific computing (or Computational science) is the field of study concerned with constructing mathematical models and numerical solution techniques and using computers to analyse and solve scientific and engineering problems. In practical use, it is typically the application of computer simulation and other forms of computation to problems in various scientific disciplines. The field is distinct from computer science (the mathematical study of computation, computers and information processing). 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 computers. Scientists and engineers develop computer programs, application software, that model systems being studied and run these programs with various sets of input parameters. Typically, these models require massive amounts of calculations (usually floating-point) and are often executed on supercomputers or distributed computing platforms. Numerical analysis is an important technique used in scientific computing. Numerical simulations have different objectives depending on the nature of the task being simulated: (1): Reconstruct and understand known events (e.g., earthquake, tsunamis and other natural disasters). (2): Optimise known scenarios (e.g., technical and manufacturing processes). (3): Predict future or unobserved situations (e.g., weather, sub-atomic particle behaviour). Algorithms and mathematical methods used in scientific computing are varied. Commonly applied methods include: (1): Numerical analysis (2): Application of Taylor series as convergent and asymptotic series (3): Computing derivatives by finite differences High order difference approximations via Taylor series and Richardson extrapolation (4): Methods for integration on a uniform mesh: rectangle rule, trapezoid rule, midpoint rule, Simpson's rule (5): Runge Kutta method for solving ordinary differential equations (6): Monte Carlo methods (7): Numerical Linear Algebra (8): Computing the factors by Gauss elimination (9): Choleski factorizations (10): Discrete Fourier transform and applications. (11): Newton's method (12): Time stepping methods for dynamical systems Programming languages commonly used for the more mathematical aspects of scientific computing applications include Fortran, APL, MATLAB, Mathematica and PDL. The more computationally-intensive aspects of scientific computing will often leverage C/C++. Computational science application programs often model real-world changing conditions, such as weather, air flow around a plane, automobile body distortions in a crash, the motion of stars in a galaxy, an explosive device, etc. Such programs might create a 'logical mesh' in computer memory where each item corresponds to an area in space and contains information about that space relevant to the model. For example in weather models, each item might be a square kilometer; with land elevation, current wind direction, humidity, temperature, pressure, etc. The program would calculate the likely next state based on the current state, in simulated time steps, solving equations that describe how the system operates; and then repeats the process to calculate the next state. The term computational scientist is used to describe someone skilled in 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 or engineering. Scientific computing has increasingly also impacted on other areas including economics, biology and medicine. Computational science may be considered as a new third mode of science, complimenting and adding to experimentation/observation and theory. This is a thesis of Stephen Wolfram (A New Kind of Science), and of Jürgen Schmidhuber. From: http://en.wikipedia.org/wiki/Scientific_computing [ Last edited by mainpro on 2006-5-6 at 00:00 ] |
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