6#ifndef THEORETICA_ODE_H
7#define THEORETICA_ODE_H
9#include "../algebra/vec.h"
22 template<
typename Vector = vec<real>>
49#ifndef THEORETICA_NO_PRINT
54 if (
t.
size() !=
x.size()) {
59 std::stringstream
res;
61 for (
unsigned int i = 0; i <
t.
size(); ++i) {
65 for (
unsigned int j = 0;
j <
x[i].size(); ++
j) {
69 if(
j !=
x[i].size() - 1)
81 inline operator std::string() {
90 return out <<
obj.to_string();
122 template<
typename Vector>
139 template<
typename Vector,
typename OdeFunction = ode_function<Vector>>
142 return x +
h * f(t, x);
155 template<
typename Vector,
typename OdeFunction = ode_function<Vector>>
158 return x +
h * f(t +
h / 2.0, x + f(t, x) *
h / 2.0);
171 template<
typename Vector,
typename OdeFunction = ode_function<Vector>>
177 return x + (f(t, x) + f(
t_new,
x_p)) * (
h / 2.0);
191 template<
typename Vector,
typename OdeFunction = ode_function<Vector>>
211 template<
typename Vector,
typename OdeFunction = ode_function<Vector>>
221 return x + (
k1 +
k2 * 2.0 +
k3 * 2.0 +
k4) * (
h / 6.0);
235 template<
typename Vector,
typename OdeFunction = ode_function<Vector>>
240 const Vector k3 = f(t + (
h * 2.0 / 3.0), x +
h * (-
k1 / 3.0 +
k2));
243 return x + (
k1 + 3.0 *
k2 + 3.0 *
k3 +
k4) * (
h / 8.0);
257 template<
typename Vector,
typename OdeFunction = ode_function<Vector>>
262 return x1 +
h * ((3. / 2.) * f(
t1,
x1) - f(
t0,
x0) / 2.);
276 template<
typename Vector,
typename OdeFunction = ode_function<Vector>>
282 (23. / 12.) * f(
t2,
x2) - (4. / 3.) * f(
t1,
x1) + (3. / 8.) * f(
t0,
x0)
334 for (i = 1; i <=
steps; ++i) {
void resize(size_t n) const
Compatibility function to allow for allocation or resizing of dynamic vectors.
Definition vec.h:416
TH_CONSTEXPR unsigned int size() const
Returns the size of the vector (N)
Definition vec.h:406
#define TH_MATH_ERROR(F_NAME, VALUE, EXCEPTION)
TH_MATH_ERROR is a macro which throws exceptions or modifies errno (depending on which compiling opti...
Definition error.h:219
Vector step_euler(OdeFunction f, const Vector &x, real t, real h=0.0001)
Compute one step of Euler's method for ordinary differential equations.
Definition ode.h:140
Vector step_k38(OdeFunction f, const Vector &x, real t, real h=0.001)
Compute one step of Kutta's 3/8 rule method for ordinary differential equations.
Definition ode.h:236
ode_solution_t< vec4 > ode_solution4d
The solution of an ODE in 4 variables.
Definition ode.h:114
Vector step_rk2(OdeFunction f, const Vector &x, real t, real h=0.001)
Compute one step of the Runge-Kutta method of 2nd order for ordinary differential equations.
Definition ode.h:192
std::function< Vector(real, const Vector &)> ode_function
A function representing a system of differential equations, taking as input the time (independent var...
Definition ode.h:123
Vector step_adams3(OdeFunction f, const Vector &x0, real t0, const Vector &x1, real t1, const Vector &x2, real t2, real h=0.001)
Compute one step of the Adams-Bashforth linear multistep method of 3rd order for ordinary differentia...
Definition ode.h:277
ode_solution_t< Vector > solve_midpoint(OdeFunction f, const Vector &x0, real t0, real tf, real stepsize=0.0001)
Integrate an ordinary differential equation over a certain domain with the given initial conditions u...
Definition ode.h:388
Vector step_adams2(OdeFunction f, const Vector &x0, real t0, const Vector &x1, real t1, real h=0.001)
Compute one step of the Adams-Bashforth linear multistep method of 2nd order for ordinary differentia...
Definition ode.h:258
ode_solution_t< vec3 > ode_solution3d
The solution of an ODE in 3 variables.
Definition ode.h:110
ode_solution_t< vec2 > ode_solution2d
The solution of an ODE in 2 variables.
Definition ode.h:106
ode_solution_t< Vector > solve_k38(OdeFunction f, const Vector &x0, real t0, real tf, real stepsize=0.0001)
Integrate an ordinary differential equation over a certain domain with the given initial conditions u...
Definition ode.h:478
ode_solution_t< Vector > solve_rk4(OdeFunction f, const Vector &x0, real t0, real tf, real stepsize=0.01)
Integrate an ordinary differential equation over a certain domain with the given initial conditions u...
Definition ode.h:456
ode_solution_t< vec< real > > ode_solution
The solution of an ODE with any number of variables.
Definition ode.h:98
Vector step_midpoint(OdeFunction f, const Vector &x, real t, real h=0.0001)
Compute one step of the midpoint method for ordinary differential equations.
Definition ode.h:156
ode_solution_t< Vector > solve_fixstep(OdeFunction f, const Vector &x0, real t0, real tf, StepFunction step, real stepsize=0.001)
Integrate an ordinary differential equation using any numerical algorithm with a constant step size,...
Definition ode.h:312
Vector step_rk4(OdeFunction f, const Vector &x, real t, real h=0.01)
Compute one step of the Runge-Kutta method of 4th order for ordinary differential equations.
Definition ode.h:212
ode_solution_t< Vector > solve_heun(OdeFunction f, const Vector &x0, real t0, real tf, real stepsize=0.0001)
Integrate an ordinary differential equation over a certain domain with the given initial conditions u...
Definition ode.h:410
ode_solution_t< real > ode_solution1d
The solution of an ODE in 1 variable.
Definition ode.h:102
Vector step_heun(OdeFunction f, const Vector &x, real t, real h=0.001)
Compute one step of Heun's method for ordinary differential equations.
Definition ode.h:172
ode_solution_t< Vector > solve_rk2(OdeFunction f, const Vector &x0, real t0, real tf, real stepsize=0.0001)
Integrate an ordinary differential equation over a certain domain with the given initial conditions u...
Definition ode.h:433
ode_solution_t< Vector > solve_euler(OdeFunction f, const Vector &x0, real t0, real tf, real stepsize=0.0001)
Integrate an ordinary differential equation over a certain domain with the given initial conditions u...
Definition ode.h:366
Main namespace of the library which contains all functions and objects.
Definition algebra.h:27
double real
A real number, defined as a floating point type.
Definition constants.h:198
dual2 abs(dual2 x)
Compute the absolute value of a second order dual number.
Definition dual2_functions.h:198
std::remove_reference_t< decltype(std::declval< Structure >()[0])> vector_element_t
Extract the type of a vector (or any indexable container) from its operator[].
Definition core_traits.h:134
constexpr real MACH_EPSILON
Machine epsilon for the real type.
Definition constants.h:207
real nan()
Return a quiet NaN number in floating point representation.
Definition error.h:54
TH_CONSTEXPR int floor(real x)
Compute the floor of x Computes the maximum integer number that is smaller than x.
Definition real_analysis.h:271
The base type for the solution of an ODE, holding a vector of the values of the time (independent va...
Definition ode.h:23
friend std::ostream & operator<<(std::ostream &out, const ode_solution_t< Vector > &obj)
Stream the ODE solution in string representation to an output stream (std::ostream)
Definition ode.h:88
vec< real > t
A vector of the time values (independent variable).
Definition ode.h:26
ode_solution_t(size_t steps, const Vector &x0, real t0)
Prepare the structure for integration by specifying the number of total steps and the initial conditi...
Definition ode.h:39
ode_solution_t()
Default constructor.
Definition ode.h:33
std::string to_string(const std::string &separator=" ") const
Convert the ODE solution to string representation.
Definition ode.h:52
vec< Vector > x
A vector of the phase space values (dependent variable).
Definition ode.h:29