tanaka2_formula.h

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/*
 * Copyright 2021 MusicScience37 (Kenta Kabashima)
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
#pragma once
 
#include "num_collect/base/index_type.h"
#include "num_collect/logging/log_tag_view.h"
#include "num_collect/ode/concepts/problem.h"
#include "num_collect/ode/concepts/slope_equation_solver.h"
#include "num_collect/ode/embedded_solver.h"
#include "num_collect/ode/inexact_newton_slope_equation_solver.h"
#include "num_collect/ode/runge_kutta/implicit_formula_base.h"
 
namespace num_collect::ode::runge_kutta {
 
template <concepts::problem Problem,
    concepts::slope_equation_solver FormulaSolver =
        inexact_newton_slope_equation_solver<Problem>>
class tanaka2_formula
    : public implicit_formula_base<tanaka2_formula<Problem, FormulaSolver>,
          Problem, FormulaSolver> {
public:
    using this_type = tanaka2_formula<Problem, FormulaSolver>;
 
    using base_type =
        implicit_formula_base<tanaka2_formula<Problem, FormulaSolver>, Problem,
            FormulaSolver>;
 
    using typename base_type::problem_type;
    using typename base_type::scalar_type;
    using typename base_type::variable_type;
 
    static_assert(!problem_type::allowed_evaluations.mass,
        "Mass matrix is not supported.");
 
    using base_type::base_type;
    using base_type::problem;
 
protected:
    using base_type::coeff;
    using base_type::formula_solver;
 
public:
    static constexpr index_type stages = 3;
 
    static constexpr index_type order = 4;
 
    static constexpr index_type lesser_order = 2;
 
    static constexpr auto log_tag =
        logging::log_tag_view("num_collect::ode::runge_kutta::tanaka2_formula");
 
    static constexpr scalar_type a11 = coeff(133, 100);
    static constexpr scalar_type a21 = coeff(-5400, 18167);
    static constexpr scalar_type a22 = coeff(28967, 36334);
    static constexpr scalar_type a31 = coeff(133, 50);
    static constexpr scalar_type a32 = coeff(-108, 25);
    static constexpr scalar_type a33 = coeff(133, 100);
 
    static constexpr scalar_type b1 = coeff(133, 100);
    static constexpr scalar_type b2 = coeff(1, 2);
    static constexpr scalar_type b3 = coeff(-33, 100);
 
    static constexpr scalar_type c1 = coeff(1250, 20667);
    static constexpr scalar_type c2 = coeff(18167, 20667);
    static constexpr scalar_type c3 = coeff(1250, 20667);
 
    static constexpr scalar_type cw2 = coeff(1);
 
    static constexpr scalar_type ce1 = c1;
    static constexpr scalar_type ce2 = c2 - cw2;
    static constexpr scalar_type ce3 = c3;
 
    void step(scalar_type time, scalar_type step_size,
        const variable_type& current, variable_type& estimate) {
        variable_type unused;
        step_embedded(time, step_size, current, estimate, unused);
    }
 
    void step_embedded(scalar_type time, scalar_type step_size,
        const variable_type& current, variable_type& estimate,
        variable_type& error) {
        formula_solver().update_jacobian(
            problem(), time + b1 * step_size, step_size, current, a11);
        k1_ = problem().diff_coeff();
        formula_solver().init(k1_);
        formula_solver().solve();
 
        formula_solver().update_jacobian(problem(), time + b2 * step_size,
            step_size, current + step_size * a21 * k1_, a22);
        k2_ = problem().diff_coeff();
        formula_solver().init(k2_);
        formula_solver().solve();
 
        formula_solver().update_jacobian(problem(), time + b3 * step_size,
            step_size, current + step_size * (a31 * k1_ + a32 * k2_), a33);
        k3_ = problem().diff_coeff();
        formula_solver().init(k3_);
        formula_solver().solve();
 
        estimate = current + step_size * (c1 * k1_ + c2 * k2_ + c3 * k3_);
        error = step_size * (ce1 * k1_ + ce2 * k2_ + ce3 * k3_);
    }
 
private:
    variable_type k1_{};
    variable_type k2_{};
    variable_type k3_{};
};
 
template <concepts::problem Problem>
using tanaka2_solver = embedded_solver<tanaka2_formula<Problem>>;
 
}  // namespace num_collect::ode::runge_kutta