mathematics::equations Namespace Reference

namespace for equation solving namespace More...

Functions
auto	successive_approximations_finding_root (double(*f_eq)(double), double x0, int n) -> double
	Function for solving equations by the method of successive approximations. More...
auto	half_division_finding_root (double(*f_hd_eq)(double), double a, double b, double dx) -> double
	Function for solving equations by the method of half division. More...
auto	f_hd_eq (double x) -> double
	Function f for determining the right side of solved equations (half division) More...
auto	g_hd_eq (double x) -> double
	Function g for determining the right side of solved equations (half division) More...
auto	h_hg_eq (double x) -> double
	Function h for determining the right side of solved equations (half division) More...
auto	f_eq (double x) -> double
	Function f for determining the right side of solved equations. More...
auto	g_eq (double x) -> double
	Function g for determining the right side of solved equations. More...
auto	h_eq (double x) -> double
	Function h for determining the right side of solved equations. More...

Detailed Description

namespace for equation solving namespace

#include <cmath>
#include <iostream>
#include <string>
 
#include "libnumerixpp/core/common.hpp"
#include "libnumerixpp/libnumerixpp.hpp"
#include "libnumerixpp/mathematics/equations.hpp"
 
void test_eq_sa(double (*f_eq)(double), double x0, const std::string &eq) {
    int const iterations = 100;
 
    double z = NAN;
 
    std::cout << "Equation solution " << eq << ":\t";
 
    z = mathematics::equations::successive_approximations_finding_root(f_eq, x0, iterations);
 
    std::cout << z << '\n';
 
    std::cout << "Check finding solution:\t";
 
    std::cout << z << " = " << f_eq(z) << '\n';
 
    for (int i = 0; i <= 50; i++) {
        std::cout << "-";
    }
 
    std::cout << '\n';
}
 
auto main() -> int {
    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()

auto mathematics::equations::f_eq

(

double

x

)

-> double

Function f for determining the right side of solved equations.

Parameters

[in]

x

x value

Returns

value

f_hd_eq()

auto mathematics::equations::f_hd_eq

(

double

x

)

-> double

Function f for determining the right side of solved equations (half division)

Parameters

[in]

x

x value

Returns

value

g_eq()

auto mathematics::equations::g_eq

(

double

x

)

-> double

Function g for determining the right side of solved equations.

Parameters

[in]

x

x value

Returns

value

g_hd_eq()

auto mathematics::equations::g_hd_eq

(

double

x

)

-> double

Function g for determining the right side of solved equations (half division)

Parameters

[in]

x

x value

Returns

value

h_eq()

auto mathematics::equations::h_eq

(

double

x

)

-> double

Function h for determining the right side of solved equations.

Parameters

[in]

x

x value

Returns

value

h_hg_eq()

auto mathematics::equations::h_hg_eq

(

double

x

)

-> double

Function h for determining the right side of solved equations (half division)

Parameters

[in]

x

x value

Returns

value

half_division_finding_root()

auto mathematics::equations::half_division_finding_root	(	double(*)(double)	f_hd_eq,
		double	a,
		double	b,
		double	dx
	)		-> double

Function for solving equations by the method of half division.

The half division method for solving an algebraic equation of the form f(x) = 0 implies that the sought root is localized in the interval a <= x <= b, and at the boundaries of the root search interval the function f(x) must take values of different signs (which can be written as the condition f(a)f(b) < 0).

Parameters

[in]	f_hd_eq	The f_eq function for half division
[in]	a	a value
[in]	b	b value
[in]	dx	dx value

Returns

equation root

successive_approximations_finding_root()

auto mathematics::equations::successive_approximations_finding_root	(	double(*)(double)	f_eq,
		double	x0,
		int	n
	)		-> double

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