solve.hpp

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// -------------------------------------------------------//
//
// SHAMROCK code for hydrodynamics
// Copyright (c) 2021-2026 Timothée David--Cléris <tim.shamrock@proton.me>
// SPDX-License-Identifier: CeCILL Free Software License Agreement v2.1
// Shamrock is licensed under the CeCILL 2.1 License, see LICENSE for more information
//
// -------------------------------------------------------//
 
#pragma once
 
#include <cmath>
#include <functional>
 
namespace shammath {
 
    template<class T>
    float newton_rhaphson(std::function<T(T)> &&f, std::function<T(T)> &&df, T epsilon_c, T x_0) {
 
        auto iterate_newton = [](T f, T df, T xk) -> T {
            return xk - (f / df);
        };
 
        T xk      = x_0;
        T epsilon = 100000;
 
        while (epsilon > epsilon_c) {
            T xkp1 = iterate_newton(f(xk), df(xk), xk);
 
            epsilon = std::fabs(xk - xkp1);
 
            xk = xkp1;
        }
 
        return xk;
    }
 
} // namespace shammath