Namespace integrator

namespace integrator

Numerical methods for differential equations.

Numerical methods for simulating the time evolution of deterministic and stochastic ordinary nonlinear differential equations. All integrators compute a single step of the solution.

Author

Oliver Laslett

Date

2017

Functions

void rk4(double *next_state, double *k1, double *k2, double *k3, double *k4, const double *current_state, const std::function<void(double *, const double *, const double)> derivs, const size_t n_dims, const double t, const double h, )

void heun(double *next_state, double *drift_arr, double *trial_drift_arr, double *diffusion_matrix, double *trial_diffusion_matrix, const double *current_state, const double *wiener_steps, const std::function<void(double *, double *, const double *, const double)> sde, const size_t n_dims, const size_t wiener_dims, const double t, const double step_size, )

void eulerm(double *states, double *diffusion_matrix, const double *initial_state, const double *wiener_process, const std::function<void(double *, const double *, const double)> drift, const std::function<void(double *, const double *, const double)> diffusion, const size_t n_dims, const size_t n_wiener, const double t, const double step_size, )

template <class CSTATES, class CDIFF>

void milstein(CSTATES &next_state, const CSTATES &current_state, const CSTATES &drift, const CDIFF &diffusion, const CSTATES &wiener_increments, const double step_size)

int implicit_midpoint(double *x, double *dwm, double *a_work, double *b_work, double *adash_work, double *bdash_work, double *x_guess, double *x_opt_tmp, double *x_opt_jac, lapack_int *x_opt_ipiv, const double *x0, const double *dw, const std::function<void(double *, double *, double *, double *, const double *, const double, const double)> sde, const size_t n_dim, const size_t w_dim, const double t, const double dt, const double eps, const size_t max_iter, )

void rk45(double *next_state, double *temp_state, double *k1, double *k2, double *k3, double *k4, double *k5, double *k6, double *h_ptr, double *t_ptr, const double *current_state, const std::function<void(double *, const double *, const double)> ode, const size_t n_dims, const double eps, )

RK45 Cash-Karp adaptive step deterministic ODE solver.

Solves ODEs :) returns the next state and the time step to be used in the next instance what about the actual time step that it used? That’s also important!

namespace ck_butcher_table

Cash-Karp parameter table for RK45.

Variables

constexpr double c11 = 0.2

constexpr double c21 = 3.0/40.0

constexpr double c22 = 9.0/40.0

constexpr double c31 = 3.0/10.0

constexpr double c32 = -9.0/10.0

constexpr double c33 = 6.0/5.0

constexpr double c41 = -11.0/54.0

constexpr double c42 = 2.5

constexpr double c43 = -70.0/27.0

constexpr double c44 = 35.0/27.0

constexpr double c51 = 1631.0/55296.0

constexpr double c52 = 175.0/512.0

constexpr double c53 = 575.0/13824.0

constexpr double c54 = 44275.0/110592.0

constexpr double c55 = 253.0/4096.0

constexpr double hc1 = 0.2

constexpr double hc2 = 0.3

constexpr double hc3 = 0.6

constexpr double hc4 = 1.0

constexpr double hc5 = 7.0/8.0

constexpr double x11 = 37.0/378.0

constexpr double x13 = 250.0/621.0

constexpr double x14 = 125.0/594.0

constexpr double x16 = 512.0/1771.0

constexpr double x21 = 2825.0/27648.0

constexpr double x23 = 18575.0/48384.0

constexpr double x24 = 13525.0/55296.0

constexpr double x25 = 277.0/14336.0

constexpr double x26 = 0.25