Educational_practice

2-nd semester educational practice

The program has an intuitive text interface

The project consists of three modules, each module solves one of the tasks below:

• Solving nonlinear equations
• Interpolation
• Numerical integration

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Nonlinear equations

Method: Newton 's method

Steps:

1. Getting a function
2. Plotting the function
3. Setting the boundaries of the root search
4. Setting the search error
5. Solving
   • Using the developed function
     • Determination of the 1st and 2nd derivative at point a
     • Checking for monotony and convexity
     • Cyclic root search until the required accuracy is achived
   • Using the built-in function
6. Output of the results

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Interpolation

Method: Lagrange interpolation polynomial

Steps:

1. Getting a vector of arguments
2. Getting a vector of values
3. Solving
   • Using the developed function
     • Initialization of the vector of coefficients of the polynomial
     • Summation of products of values (y(i)) with corresponding products of fractions (lix(x,i))
     • Converting a vector of coefficients to function handle
4. Search and output to the console values for the desired points
5. Plotting the function
   • Calculated by the developed function
6. Solving
   • Using the built-in functions
7. Search and output to the console values for the desired points
8. Plotting the function
   • Calculated by the built-in function

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Integration

Method: trapezoid method

Steps:

1. Getting the integrand funtion
2. Setting the lower and upper limits of integration
3. Setting the error of calculating the integral
4. Solving
   • Using the developed function
     • Setting the integration step
     • Cyclic calculation until the desired accuracy is achieved
     • Construction of grid nodes on a segment with a given step
     • Search for the second derivative for the following error calculation
     • Initializing of a variable storing the sum of trapezoid areas
     • Calculation the trapezoid area and adding this value to the 'area' variable
     • Searching the largest second derivative
     • Calculation of the error of integral calculations
     • Checking for sufficient accuracy
     • Decreasing the integration step, according to the Runge rule
5. Output of the result and the actual error for the developed function
6. Solving
   • Using built-in function
7. Output of result calculated by the built-in function

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Author information

>> info_prog
Программа 'MyLib'
Назначение: автоматизация математических задач
(Решение нелинейных уравнений, интерполяция, интегрирование)
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В программе используются следующие методы решений:
Нелинейные уравнения - метод Ньютона
Интерполяция - метод Лагранжа
Интегрирование - метод трапеций
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Последняя редакция: 21.04.2023
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Разработчик:
Куриш Михаил Викторович
ГУАП, гр №4232
kypten.wave@gmail.com
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