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Numerical analysis is applied in many branches of science and engineering, including celestial mechanics, space physics, quantum mechanics, fluid dynamics, atmospheric science, oceanography, climatology, geophysics, seismology, geomechanics, structural dynamics, mathematics, and many others. Often, the numerical methods used in these areas involve a sequence of iterative procedures, which are then called numerical algorithms. They use approximations to mathematical analysis and aim at producing numerical solutions to the problems of interest. Since the early 1970s, a diverse range of numerical analysis, often called numerical analysis, has been developed, which includes, for example, computers for doing numerical computations, and statistics to study the results of such computations. Numerical analysis also has been applied to financial mathematics and economics, known as financial engineering.
The differences between engineering and scientific methods are that in engineering there is usually a specific application that is being addressed, whereas in the scientific method one can explore a range of possible situations by varying model assumptions and studying the results of the model. For instance, the model of a mechanical problem may be constructed to accurately represent the physical situation, but it may be that the model is too complex for a particular solution to be obtained, so one may decide to change some of the assumptions about the situation to help to obtain a solution. The model may be simplified, expanded, or changed to represent a different situation, and the process is repeated until a solution is obtained. This is a typical scientific method. 827ec27edc