allpix::tableau

Functions

	Name
const auto	RK3((Eigen::Matrix< double, 5, 3 >()« 0, 0, 0, 1.0/2, 0, 0, -1, 2, 0, 1.0/6, 2.0/3, 1.0/6, 0, 0, 0).finished() ) Kutta’s third order method.
const auto	RK4((Eigen::Matrix< double, 6, 4 >()« 0, 0, 0, 0, 1.0/2, 0, 0, 0, 0, 1.0/2, 0, 0, 0, 0, 1, 0, 1.0/6, 1.0/3, 1.0/3, 1.0/6, 0, 0, 0, 0).finished() ) Classic original Runge-Kutta method.
const auto	RK5((Eigen::Matrix< double, 8, 6 >()« 0, 0, 0, 0, 0, 0, 1.0/4, 0, 0, 0, 0, 0, 3.0/32, 9.0/32, 0, 0, 0, 0, 1932.0/2197, -7200.0/2197, 7296.0/2197, 0, 0, 0, 439.0/216, -8, 3680.0/513, -845.0/4104, 0, 0, -8.0/27, 2, -3544.0/2565, 1859.0/4104, -11.0/40, 0, 16.0/135, 0, 6656.0/12825, 28561.0/56430, -9.0/50, 2.0/55, 25.0/216, 0, 1408.0/2565, 2197.0/4104, -1.0/5, 0).finished() ) Runge-Kutta-Fehlberg method Values from https://ntrs.nasa.gov/citations/19680027281, p.13, Table III.
const auto	RKCK((Eigen::Matrix< double, 8, 6 >()« 0, 0, 0, 0, 0, 0, 1.0/5, 0, 0, 0, 0, 0, 3.0/40, 9.0/40, 0, 0, 0, 0, 3.0/10, -9.0/10, 6.0/5, 0, 0, 0, -11.0/54, 5.0/2, -70.0/27, 35.0/27, 0, 0, 1631.0/55296, 175.0/512, 575.0/13824, 44275.0/110592, 253.0/4096, 0, 37.0/378, 0, 250.0/621, 125.0/594, 0, 512.0/1771, 2825.0/27648, 0, 18575.0/48384, 13525.0/55296, 277.0/14336, 1.0/4).finished() ) Runge-Kutta-Cash-Karp method.

Functions Documentation

function RK3

static const auto RK3(
    (Eigen::Matrix< double, 5, 3 >()<< 0, 0, 0, 1.0/2, 0, 0, -1, 2, 0, 1.0/6, 2.0/3, 1.0/6, 0, 0, 0).finished() 
)

Kutta’s third order method.

Warning: Without error function

function RK4

static const auto RK4(
    (Eigen::Matrix< double, 6, 4 >()<< 0, 0, 0, 0, 1.0/2, 0, 0, 0, 0, 1.0/2, 0, 0, 0, 0, 1, 0, 1.0/6, 1.0/3, 1.0/3, 1.0/6, 0, 0, 0, 0).finished() 
)

Classic original Runge-Kutta method.

Warning: Without error function

function RK5

static const auto RK5(
    (Eigen::Matrix< double, 8, 6 >()<< 0, 0, 0, 0, 0, 0, 1.0/4, 0, 0, 0, 0, 0, 3.0/32, 9.0/32, 0, 0, 0, 0, 1932.0/2197, -7200.0/2197, 7296.0/2197, 0, 0, 0, 439.0/216, -8, 3680.0/513, -845.0/4104, 0, 0, -8.0/27, 2, -3544.0/2565, 1859.0/4104, -11.0/40, 0, 16.0/135, 0, 6656.0/12825, 28561.0/56430, -9.0/50, 2.0/55, 25.0/216, 0, 1408.0/2565, 2197.0/4104, -1.0/5, 0).finished() 
)

Runge-Kutta-Fehlberg method Values from https://ntrs.nasa.gov/citations/19680027281, p.13, Table III.

function RKCK

static const auto RKCK(
    (Eigen::Matrix< double, 8, 6 >()<< 0, 0, 0, 0, 0, 0, 1.0/5, 0, 0, 0, 0, 0, 3.0/40, 9.0/40, 0, 0, 0, 0, 3.0/10, -9.0/10, 6.0/5, 0, 0, 0, -11.0/54, 5.0/2, -70.0/27, 35.0/27, 0, 0, 1631.0/55296, 175.0/512, 575.0/13824, 44275.0/110592, 253.0/4096, 0, 37.0/378, 0, 250.0/621, 125.0/594, 0, 512.0/1771, 2825.0/27648, 0, 18575.0/48384, 13525.0/55296, 277.0/14336, 1.0/4).finished() 
)

Runge-Kutta-Cash-Karp method.

Updated on 2024-12-13 at 08:31:36 +0000