sm::rungekutta4

A fourth order Runge Kutta solver class

import sm.rungekutta4;

Module file: sm/rungekutta4.cppm. Test code: tests/arungekutta4_1

Table of Contents

• Summary
• Usage
  • Single ODE setup
  • Multiple ODE setup
  • Finding solutions

Summary

A fourth order Runge Kutta solver class with a fixed (i.e. non-adaptive) step size.

Usage

You first instantiate your sm::rungekutta4, giving it the function dx/dt, the initial state (x0), time (usually 0) and a step size. You can then advance the state by a single step with sm::rungekutta4::step() or find a time series of solutions with sm::rungekutta4::integrate().

Single ODE setup

x and t have scalar type, such as double.

auto dxdt = [](const double& t, const double& x) { return -x; };
double x0 = 1.0; // Initial state x(t0)
double t0 = 0.0; // Initial time
double h = 0.01; // step size
sm::rungekutta4<double> rks (dxdt, x0, t0, h);
// Can now rks.step(); or rk.integrate(...);

Alternatively, use a default constructor, and the sm::rungekutta4::init() method:

sm::rungekutta4<double> rks;
rks.init (dxdt, x0, t0, h);

Multiple ODE setup

t and h still have scalar type, such as float, but the state x may be sm::vec<> or sm::vvec<>.

auto dxdt = [](const float& t, const sm::vec<float, 2>& x) {
                return sm::vec<float, 2>{ x[1], -x[0] };
            };
sm::vec<float, 2> x0 = {1, 0};
float t0 = 0.0f;
float h = 0.01f;
sm::rungekutta4<float, sm::vec<float, 2>> rkm (dxdt, x0, t0, h);

Finding solutions

Either step forwards for each timestep with rungekutta4::step() or call integrate:

sm::vvec<double> traj_s = rks.integrate (100);
sm::vvec<sm::vec<float, 2>> traj_m = rkm.integrate (1000);