mathematics::equations Namespace Reference

namespace for equation solving namespace More...

Functions
double	successiveApproximationsFindingRoot (double(*f_eq)(double), double x0, int n)
	Function for solving equations by the method of successive approximations. More...
double	f_eq (double x)
	Function f for determining the right side of solved equations. More...
double	g_eq (double x)
	Function g for determining the right side of solved equations. More...
double	h_eq (double x)
	Function h for determining the right side of solved equations. More...

Detailed Description

namespace for equation solving namespace

#include <iostream>
#include <string>
 
#include "libnumerixpp/core/common.hpp"
#include "libnumerixpp/libnumerixpp.hpp"
#include "libnumerixpp/mathematics/core.hpp"
#include "libnumerixpp/mathematics/equations.hpp"
 
void test_eq_sa(double (*f_eq)(double), double x0, std::string eq) {
    int iterations = 100;
 
    double z;
 
    std::cout << "Equation solution " << eq << ":\t";
 
    z = mathematics::equations::successiveApproximationsFindingRoot(f_eq, x0, iterations);
 
    std::cout << z << std::endl;
 
    std::cout << "Check finding solution:\t";
 
    std::cout << z << " = " << f_eq(z) << std::endl;
 
    for (int i = 0; i <= 50; i++) {
        std::cout << "-";
    }
 
    std::cout << std::endl;
}
 
int main() {
    credits();
    println("LIBNUMERIXPP");
 
    test_eq_sa(mathematics::equations::f_eq, 0, "x=0.5cos(x)");
    test_eq_sa(mathematics::equations::g_eq, 0, "x=exp(-x)");
    test_eq_sa(mathematics::equations::h_eq, 1, "x=(x*x+6)/5");
 
    return 0;
}

Function Documentation

f_eq()

double mathematics::equations::f_eq

(

double

x

)

Function f for determining the right side of solved equations.

Parameters

[in]

x

x value

Returns

value

g_eq()

double mathematics::equations::g_eq

(

double

x

)

Function g for determining the right side of solved equations.

Parameters

[in]

x

x value

Returns

value

h_eq()

double mathematics::equations::h_eq

(

double

x

)

Function h for determining the right side of solved equations.

Parameters

[in]

x

x value

Returns

value

successiveApproximationsFindingRoot()

double mathematics::equations::successiveApproximationsFindingRoot	(	double(*)(double)	f_eq,
		double	x0,
		int	n
	)

Function for solving equations by the method of successive approximations.

When solving an equation ( \(x = \Phi(x)\)), under some additional conditions, the method of successive approximations can be used. Its essence boils down to the fact that the initial position x0 is specified for the root of the equation, after which, using an iterative procedure, each subsequent approximation is calculated based on the previous one in accordance with the formula \(x_{n + 1} = \Phi(x_{n})\). Example equations: \(x = 0,5 * \cos(x)\); \(x = \exp(-x)\); \(x = (x^{2} + 6) / 5\).

Parameters

[in]	f	The f
[in]	x0	The x 0
[in]	n	n value

Returns

equation root