Numerical Methods

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Numerical Methods


in mathematics, methods of approximate solution of mathematical problems through the performance of a finite number of elementary operations on numbers.

The elementary operations used are arithmetic operations, generally carried out approximately, and subsidiary operations, such as recording intermediate results and extracting information from tables. Numbers are expressed by a limited set of digits in some positional numeration system, for example, the decimal or binary system. The number line is thus replaced by a discrete system of numbers, sometimes called a net. A function of a continuous variable accordingly is replaced by a table of the function’s values in this discrete system of numbers (seeMATHEMATICALTABLE). Operations of analysis that act on continuous functions are replaced by algebraic operations on the function’s values in the table. Numerical methods reduce the solution of mathematical problems to computations that can be performed manually or by means of calculating machines. The development of new numerical methods and their use in computers have led to the rise of computer mathematics.

References in periodicals archive ?
In a textbook that can be used for self-study or in a classroom, Ayyub and McCuen introduce numerical methods to engineering students and practicing engineers; emphasize the practical aspects of the use of these methods; and establish their limitations, advantages, and disadvantages.
Saguet explains the transmission line matrix (TLM) method, one of the time-domain numerical methods, and how it can be used to analyze systems in electromagnetics.
of Tennessee, Chattanooga) text is unique in combining numerical methods and computer programming--Visual Basic Application (VBA)--in a single book for undergraduate engineering and computer science students.
There are several analytical methods used to solve very special, mostly linear, fractional differential equations, says mathematicians Li and Zeng, and they focus mainly on numerical methods for fractional integrals, fractional derivatives, and fractional differential equations.
Among the topics are experimental and numerical methods for calculating hydrodynamic profiles, the knowledge base in interpreting collision regulations at sea, uncertainty in analytical collision dynamics models due to assumptions in dynamic parameters, solutions to direct geodetic problems in navigational applications, and a position reference system for flight inspection aircraft.
The book can also be used in graduate courses in finite element methods, numerical methods for partial differential equations, numerical analysis, and scientific computing.
In this second edition they enlarge the scope to include the design of robust and optimal controllers, and add a lot of new material on numerical methods to encompass other research communities, particularly the numerical linear algebra and the numerical optimization communities.

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