rungekutta.cpp File Reference

Runge Kutta fourth order method implementation More...

#include <cassert>
#include <iostream>
#include <vector>

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Namespaces
	numerical_methods
	for io operations
	runge_kutta
	Functions for Runge Kutta fourth order method.

Functions
double	numerical_methods::runge_kutta::rungeKutta (double init_x, const double &init_y, const double &x, const double &h)
	the Runge Kutta method finds the value of integration of a function in the given limits. the lower limit of integration as the initial value and the upper limit is the given x More...
static double	change (double x, double y)
	for using the vector container More...
static void	test ()
	Tests to check algorithm implementation. More...
int	main ()
	Main function. More...

Detailed Description

Runge Kutta fourth order method implementation

Author

Rudra Prasad Das

It solves the unknown value of y for a given value of x only first order differential equations can be solved

Function Documentation

change()

static double change ( double  x, double  y  )

static

for using the vector container

asserting the test functions for io operations

The change() function is used to return the updated iterative value corresponding to the given function

Parameters

x	is the value corresponding to the x coordinate
y	is the value corresponding to the y coordinate

Returns

the computed function value at that call

Examples

/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp.

{ return ((x - y) / 2.0); }

main()

int main

(

void

)

Main function.

Returns

0 on exit

           {
    test();  // Execute the tests
    return 0;
}

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rungeKutta()

double numerical_methods::runge_kutta::rungeKutta	(	double	init_x,
		const double &	init_y,
		const double &	x,
		const double &	h
	)

the Runge Kutta method finds the value of integration of a function in the given limits. the lower limit of integration as the initial value and the upper limit is the given x

Parameters

init_x	is the value of initial x and is updated after each call
init_y	is the value of initial x and is updated after each call
x	is current iteration at which the function needs to be evaluated
h	is the step value

Returns

the value of y at thr required value of x from the initial conditions

Examples

/Users/runner/work/C-Plus-Plus/C-Plus-Plus/numerical_methods/rungekutta.cpp.

                                   {
    // Count number of iterations
    // using step size or
    // step height h
 
    // n calucates the number of iterations
    // k1, k2, k3, k4 are the Runge Kutta variables
    // used for calculation of y at each iteration
 
    auto n = static_cast<uint64_t>((x - init_x) / h);
    // used a vector container for the variables
    std::vector<double> k(4, 0.0);
 
    // Iterate for number of iterations
 
    double y = init_y;
    for (int i = 1; i <= n; ++i) {
        // Apply Runge Kutta Formulas
        // to find next value of y
        k[0] = h * change(init_x, y);
        k[1] = h * change(init_x + 0.5 * h, y + 0.5 * k[0]);
        k[2] = h * change(init_x + 0.5 * h, y + 0.5 * k[1]);
        k[3] = h * change(init_x + h, y + k[2]);
 
        // Update next value of y
 
        y += (1.0 / 6.0) * (k[0] + 2 * k[1] + 2 * k[2] + k[3]);
 
        // Update next value of x
 
        init_x += h;
    }
 
    return y;
}

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test()

static void test ( )

static

Tests to check algorithm implementation.

Returns

void

                   {
    std::cout << "The Runge Kutta function will be tested on the basis of "
                 "precomputed values\n";
 
    std::cout << "Test 1...."
              << "\n";
    double valfirst = numerical_methods::runge_kutta::rungeKutta(
        2, 3, 4, 0.2);  // Tests the function with pre calculated values
    assert(valfirst == 3.10363932323749570);
    std::cout << "Passed Test 1\n";
 
    std::cout << "Test 2...."
              << "\n";
    double valsec = numerical_methods::runge_kutta::rungeKutta(
        1, 2, 5, 0.1);  // The value of step changed
    assert(valsec == 3.40600589380261409);
    std::cout << "Passed Test 2\n";
 
    std::cout << "Test 3...."
              << "\n";
    double valthird = numerical_methods::runge_kutta::rungeKutta(
        -1, 3, 4, 0.1);  // Tested with negative value
    assert(valthird == 2.49251005860244268);
    std::cout << "Passed Test 3\n";
}