Thursday, 1 October 2020

What are the Numerical Methods



What are the Numerical Methods, the science of mathematics is a broad sea, and the basis of all the sciences that a person relies on in life? No science can be established without relying on mathematics, and mathematics includes many branches and from these branches of numerical mathematics.


Numerical analysis

Numerical analysis is one of the branches of mathematics and computer science (computer), where the numerical analysis is based on the principle of creating, analyzing, and implementing a number of algorithms (relative to Muhammad bin Musa al-Khwarizmi, a mathematician), to reach numerical solutions to mathematical problems that are built on A set of constant changes and fluctuations.


These problems may also form in the social sciences, the natural sciences, engineering, and medicine, and they may be called by other names for analysis such as quantitative analysis or numerical methods.


As a result of the tremendous growth of the digital computer, its presence in abundance, and it's being one of the basics of life, which led to an increased need to analyze mathematical models in engineering and science, in order to work to solve the complexities in these sciences. In the period (1980-1990), a system emerged that combined numerical analysis, symbolic mathematical calculations, computer graphics, and other areas of computer science.


This is in order to facilitate the creation, solution, and interpretation of complex mathematical models of the world, and in any case, the algorithm that solves.


A problem with good conditions is fixed numerically, or it may not be fixed numerically, so the matter is not only related to the nature of the problem but rather the way of solving it. Therefore, the task of numerical analysis is also to find stable algorithms to solve problems with bad conditions.


Mathematical methods in numerical analysis


  • When encountering any intractable problem that cannot be solved by direct methods, this problem can be replaced by others close to it, where it can be easily and easily solved. Examples of this method are the use of interpolation in developing methods of digital integration and exploratory methods of roots.
  • This method is done by using real analysis, functional analysis, and linear algebra.
  • In this method, the nature of the error and the problem must be understood before approximating it, as this helps to create extrapolations to improve the rate of convergence method of the numerical method.


Polynomial is used and it is an algebraic expression that contains a set of numbers and variables that are formatted according to a specific pattern, for example, the following form:


For x n, where (l) is the coefficient of x, and it belongs to the group of real numbers, (n) is the degree or power, and it belongs to the set of integers, so for the following example illustration has sensitive roots, (p (x) = (x - 1) (x - 2) (x - 3) (x - 4) (x - 5) (x - 6) (x - 7 p (x) = x7 - 28 x 6 + 322 x 5 - 1,960 X 4 - 6,769 x 3 - 13,132 x 2 + 13,068x - 5,040.

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