Scientific computing (or computational science) is the field of study concerned with constructing mathematical models and numerical solution techniques and using computers to analyze 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. A computer simulation or a computer model is a computer program that attempts to simulate an abstract model of a particular system. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...

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. Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... A Lego RCX Computer is an example of an embedded computer used to control mechanical devices. ... In general, information processing is the changing (processing) of information in any manner detectable by an observer. ... A Lego RCX Computer is an example of an embedded computer used to control mechanical devices. ...

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. A computer program (often simply called a program) is an example of computer software that prescribes the actions (computations) that are to be carried out by a computer. ... Application software is a defined subclass of computer software that employs the capabilities of a computer directly to a task that the user wishes to perform. ... This article or section is in need of attention from an expert on the subject. ... A supercomputer is a computer that leads the world in terms of processing capacity, particularly speed of calculation, at the time of its introduction. ... Distributed computing is a programming paradigm focusing on designing distributed, open, scalable, transparent, fault tolerant systems. ...

Numerical analysis is an important technique used in scientific computing. Numerical simulations have different objectives depending on the nature of the task being simulated: Numerical analysis is the study of approximate methods for the problems of continuous mathematics (as distinguished from discrete mathematics). ...

• Reconstruct and understand known events (e.g., earthquake, tsunamis and other natural disasters).
• Optimise known scenarios (e.g., technical and manufacturing processes).
• 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:

• Numerical analysis
• Application of Taylor series as convergent and asymptotic series
• Computing derivatives by Automatic differentiation (AD)
• 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 for solving ordinary differential equations
• Monte Carlo methods
• Numerical Linear Algebra
• Computing the LU factors by Gaussian elimination
• Choleski factorizations
• Discrete Fourier transform and applications.
• Newton's method
• Time stepping methods for dynamical systems

Programming languages commonly used for the more mathematical aspects of scientific computing applications include Fortran, MATLAB, GNU Octave, Num-Python, Sci-Python and PDL. The more computationally-intensive aspects of scientific computing will often utilize some variation of C or Fortran. As the degree of the Taylor series rises, it approaches the correct function. ... In mathematics and computer algebra, automatic differentiation, or AD, sometimes alternatively called algorithmic differentiation, is a method to numerically evaluate the derivative of a function specified by a computer program. ... In numerical analysis, Richardson extrapolation is a method to improve an approximation that depends on a step size. ... In numerical analysis, the Runge-Kutta methods are an important family of implicit and explicit iterative methods for the approximation of solutions of ordinary differential equations. ... Monte Carlo methods are a widely used class of computational algorithms for simulating the behavior of various physical and mathematical systems. ... In mathematics, Gaussian elimination or Gauss–Jordan elimination, named after Carl Friedrich Gauss and Wilhelm Jordan (for many, Gaussian elimination is regarded as the front half of the complete Gauss–Jordan elimination), is an algorithm in linear algebra for determining the solutions of a system of linear equations, for determining... In mathematics, the Cholesky decomposition, named after André-Louis Cholesky, is a matrix decomposition of a symmetric positive-definite matrix into a lower triangular matrix and the transpose of the lower triangular matrix. ... In mathematics, the discrete Fourier transform (DFT), sometimes called the finite Fourier transform, is a Fourier transform widely employed in signal processing and related fields to analyze the frequencies contained in a sampled signal, solve partial differential equations, and to perform other operations such as convolutions. ... In numerical analysis, Newtons method (or the Newton–Raphson method or the Newton–Fourier method) is an efficient algorithm for finding approximations to the zeros (or roots) of a real-valued function. ... Fortran (previously FORTRAN[1]) is a general-purpose[2], procedural,[3] imperative programming language that is especially suited to numeric computation and scientific computing. ... MATLAB is a numerical computing environment and programming language. ... For other uses of the word octave see Octave (disambiguation) Octave is a free computer program for performing numerical computations, which is mostly compatible with MATLAB. It is part of the GNU project. ... Python is an interpreted programming language created by Guido van Rossum in 1990. ... PDL (short for Perl Data Language) is a set of Array programming extensions to the Perl programming language. ... C is a general-purpose, procedural, imperative computer programming language developed in 1972 by Dennis Ritchie at the Bell Telephone Laboratories for use with the Unix operating system. ...

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 repeat 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. The term computational scientist is used to describe someone skilled in scientific computing. ...

Computational science is now commonly considered a third mode of science, complementing and adding to experimentation/observation and theory. This thesis has been propounded by many, including Stephen Wolfram (most notably in his book A New Kind of Science), and Jürgen Schmidhuber. Part of a scientific laboratory at the University of Cologne. ... From Latin ex- + -periri (akin to periculum attempt). ... Observation is an activity of a sapient or sentient living being, which senses and assimiliates the knowledge of a phenomenon in its framework of previous knowledge and ideas. ... The word theory has a number of distinct meanings in different fields of knowledge, depending on their methodologies and the context of discussion. ... Stephen Wolfram (born August 29, 1959 in London) is a scientist known for his work in theoretical particle physics, cellular automata, complexity theory, and computer algebra, and is the creator of the computer program Mathematica. ... A New Kind of Science is a controversial book by Stephen Wolfram, published in 2002. ... Jürgen Schmidhuber (born 1963 in Munich) is a computer scientist and artist known for his work on machine learning, universal Artificial Intelligence (AI), artificial neural networks, digital physics, and low-complexity art. ...

Education

Scientific computation is most often studied through an applied mathematics or computer science program, or within a standard mathematics, sciences, or engineering program. At some institutions a specialization in scientific computation can be earned as a "minor" within another program (which may be at varying levels). However, there are increasingly many bachelor's and master's programs in computational science. Some schools also offer the Ph.D. in computational science, computational engineering, computational science and engineering, or scientific computation. To meet Wikipedias quality standards, this article may require cleanup. ... Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... The examples and perspective in this article or section may not represent a worldwide view. ...

There are also programs in areas such as computational physics, computational chemistry, etc. Computational physics is the study and implementation of numerical algorithms in order to solve problems in physics for which a quantitative theory already exists. ... Computational chemistry is a branch of chemistry that uses the results of theoretical chemistry incorporated into efficient computer programs to calculate the structures and properties of molecules and solids, applying these programs to real chemical problems. ...

Related fields

• Bioinformatics
• Cheminformatics
• Chemometrics
• Computational chemistry
• Computational biology
• Computational mechanics
• Computational physics
• Computational Electromagnetics
• Computational fluid dynamics
• Computational economics
• Environmental simulations
• Financial modeling
• Geographic information system (GIS)
• Numerical weather prediction

Map of the human X chromosome (from the NCBI website). ... Cheminformatics is the use of computer and informational techniques, applied to a range of problems in the field of chemistry. ... Chemometrics is the application of mathematical or statistical methods to chemical data. ... Computational chemistry is a branch of chemistry that uses the results of theoretical chemistry incorporated into efficient computer programs to calculate the structures and properties of molecules and solids, applying these programs to real chemical problems. ... Bioinformatics or computational biology is the use of techniques from applied mathematics, informatics, statistics, and computer science to solve biological problems. ... Computational mechanics is the subject/profession concerned with the use of computational methods and devices to study phenomena governed by the principles of mechanics. ... Computational physics is the study and implementation of numerical algorithms in order to solve problems in physics for which a quantitative theory already exists. ... Finite-Difference Time-Domain (FDTD) is a popular electromagnetic modeling technique. ... A computer simulation of high velocity air flow around the Space Shuttle during re-entry. ... Computational economics is a form of economics which relies on mathematical methods, including mathematical economics and econometrics. ... Computation of corporate finance problems, standard portfolio problems, option pricing and applications, and duration and immunization. ... A geographic information system (GIS) is a system for creating, storing, analyzing and managing spatial data and associated attributes. ... Numerical weather prediction is the science of predicting the weather using models of the atmosphere and computational techniques. ...

External links

• Scientific Computing World
• Links to Downloadable Computational Tools
• SIAM Journal on Scientific Computing
• Scientific Computing magazine
• Brockport State College's Dept. of Computational Science
• Oregon State University's Computational Physics program (pdf)
• Wolfram Research
• Interdisciplinary school of scientific computing,UoP,India