Computers are used to solve mathematical problems in scientific research and engineering calculations, which are called "numerical calculations". Numerical computing mainly studies how to use computers to better solve various mathematical problems, including the discretization of continuous systems and the solution of discrete equations, and considers issues such as errors, convergence and stability.
The operating environment of this tutorial: Windows 7 system, Dell G3 computer.
What is a computer used to solve mathematical problems in scientific research and engineering calculations called?
Computers are used to solve mathematical problems in scientific research and engineering calculations, called "numerical calculations."
Numerical computing refers to the methods and processes of effectively using digital computers to find approximate solutions to mathematical problems, as well as the discipline composed of related theories. Numerical computing mainly studies how to use computers to better solve various mathematical problems, including the discretization of continuous systems and the solution of discrete equations, and considers issues such as errors, convergence and stability.
Research fields:
In terms of mathematical types, the research fields of numerical operations include numerical approximation, numerical differentiation and numerical integration, numerical algebra, optimization methods, numerical solutions to ordinary differential equations, and integrals Numerical solution of equations, numerical solution of partial differential equations, computational geometry, computational probability and statistics, etc. With the widespread application and development of computers, many problems in computing fields, such as computational physics, computational mechanics, computational chemistry, computational economics, etc., can be attributed to numerical calculation problems.
Important features:
1. The results of numerical calculations are discrete and must have errors. This is the main feature that distinguishes numerical calculation methods from analytical methods.
2. Pay attention to the stability of calculation. Controlling the growth momentum of errors and ensuring the stability of the calculation process is one of the core tasks of numerical calculation methods.
3. Focusing on fast calculation speed and high calculation accuracy are important features of numerical calculations.
4. Pay attention to structural proof.
5. Numerical calculation mainly uses the idea of finite approximation to perform error calculations.
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