CC BY
5
UDC: 62.278
Qiryigitov B.A.
teacher of department of chemistry and phyisics Andijan Institute of Agriculture and Agro technologies
Uzbekistan, Andijan
CHARACTERIZATION DIFFERENT METHODS OF APPROXIMATION AND INTERPOLATION AND THEIR IMPLEMENTATION IN MATHCAD AND MATLAB
Annotation: Computer modeling, as a type of technology, is currently one of the most important factors in accelerating scientific and technological progress. Today it is almost impossible to do design and calculation by hand.
Key words: computer, MathCAD, system, computer science, physics, mathematics, mechanics, astrophysics, mathematical formulas and signs.
MathCAD is a powerful software package for solving various mathematical problems with the ability to program. The MathCAD system occupies a leading position among all other mathematical systems. In addition to performing its mathematical functions, the MathCAD system is a very good text and graphic editor, in many respects not inferior to specialized programs.
MathCAD is a mathematical system in which the description of the solution of problems is set using the usual mathematical formulas and signs. The use of MathCAD in solving applied problems of a technical nature made it possible to dramatically increase the speed of calculations and the level of complexity of tasks. The skills and experience acquired during the execution will be important in graduate design, as well as engineering and scientific activities.
Computer modeling systems allow solving many issues and problems related to various industries, such as computer science, physics, mathematics, mechanics, astrophysics and others. In our case, using computer modeling systems such as MathCAD and Matlab, we investigate the mathematical model of the RLC circuit.
Using the Mathcad system, calculate the values of the functions of current in a circuit and voltage across a capacitor in a given electrical circuit under the influence of given values of current, voltage and EMF. Investigate the effect of a variable inductance on the minimum voltage across a capacitor.
In a broad sense, a numerical method is understood as a set of a discrete model implemented on a computer and a computational algorithm that allows solving a discretized problem. One and the same mathematical model can be associated with many discrete models and computational algorithms, i.e., numerical methods. When choosing a numerical method, it is necessary to take into account two groups of requirements:
• the discrete model must be adequate to the mathematical model;
• the numerical method must be correct and implementable on the computer.
To ensure the adequacy, the discrete model must have the properties of the convergence of the numerical method, the implementation of discrete analogs of conservation, and the qualitatively correct behavior of the solution. The convergence of the numerical method, for example, means that as the step of dividing the integration interval decreases, the accuracy of the numerical integration increases. Various mathematical models are expressions of physical conservation laws, therefore, for a discrete model, conservation laws must also be satisfied. Qualitatively correct behavior of a discrete model means that due to the discrete nature of the model's behavior, some details of the behavior of the real system are not lost. The correctness of the numerical method means that the discrete problem must be unambiguously solvable and resistant to errors in the initial data and calculation errors.
When using analytical methods, the solution to the problem can be expressed using formulas. In particular, if mathematically the task is to solve the simplest algebraic equations, differential equations, etc., then the use of techniques known from the course of mathematics immediately leads to the goal. Unfortunately, in practice, these are too rare cases. The main tool for solving complex mathematical problems in accordance with are numerical methods that make it possible to reduce the solution of a problem to the execution of a finite number of arithmetic operations on numbers; the results are obtained as numerical values. Many numerical methods were developed a long time ago, but when calculating manually, they could only be used to solve not too time-consuming problems. When using analytical methods, the solution to the problem can be expressed using formulas. In particular, if mathematically the task is to solve the simplest algebraic equations, differential equations, etc., then the use of techniques known from the course of mathematics immediately leads to the goal. Unfortunately, in practice, these are too rare cases.
In engineering practice, it is often necessary to obtain an analytical functional dependence from the results of an experiment given by a tabular function. This process is called approximation or approximation.
Interpolation uses the values of some function, given at a number of points, to predict the values of the function between them. In Mathcad, you can either connect data points with straight lines (linear interpolation) or connect them with cubic polynomial segments (cubic spline interpolation).
Unlike regression functions, interpolation functions define a curve that exactly passes through specified points. Linear prediction is about using existing data values to predict values outside of them. Mathcad has a function that allows you to predict future data values based on existing data.
Application of the Mathcad and Matlab system for the study of a mathematical model of an electrical one, which includes an EMF source, resistance R, capacitance C and inductor L.
Complete problem statement with the use of the Mathcad system:
• Calculate the values of the voltage functions on a capacitor in a second-order circuit with a step action E (t). Plot these functions
• Investigate the response of the oscillating circuit to external influences at various values of the variable inductance parameter. Construct graphs of functions of voltage across a capacitor for different values of a given variable parameter in one field.
• Calculate the analytical approximating function of the dependence of the minimum voltage value on the inductance according to the research results of the previous paragraph. Build graphically the original and approximating dependencies.
As a result of the work, he investigated the use of the MathCAD system for studying the mathematical model of the RLC circuit, calculated the values of the functions of the current on the coil and the voltage on the capacitor at various EMF. Has built graphs of these functions. Investigated the influence of the values of the variable parameter on the form of the voltage function in the circuit. Constructed a summary graph of all obtained stress functions in one field. An analysis of the results obtained showed that the voltage directly depends on the change in the capacitor inductance.
In the course of the completed work, a study was made of the mathematical model of the electric RLC circuit using the computer mathematics systems MathCAD and Matlab.
The use of mathematical modeling using the latest computer technology helps to greatly facilitate the most complex mathematical calculations. Over time, the latest developments in the field of computer modeling are expanding their application in a wide variety of areas of human activity.
The emergence of products such as MathCAD and Matlab and their improvement is driven by the need to perform complex mathematical calculations. These systems can greatly facilitate the work in the field of complex and time-consuming mathematical calculations.
In conclusion of this work, I studied the mathematical model of the RLC circuit, and also studied the computer modeling systems MathCAD and Matlab.
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4. Stephen Schafer. HTML, XHTML and CSS. The user's Bible, 5th edition = HTML, XHTML, and CSS Bible, 5th Edition. - Moscow: Dialectics, 2011.
