rungekutta.cpp

Go to the documentation of this file.

 
#include <cassert>   
#include <cstdint>
#include <iostream>  
#include <vector>    
static double change(double x, double y) { return ((x - y) / 2.0); }
 
namespace numerical_methods {
namespace runge_kutta {
double rungeKutta(double init_x, const double &init_y, const double &x,
                  const double &h) {
    // 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;
}
}  // namespace runge_kutta
}  // namespace numerical_methods
 
static void test() {
    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";
}
 
int main() {
    test();  // Execute the tests
    return 0;
}