@Equation

This module specifies which equations of motion to solve, and the details of how to solve them.

Types

This module has two secondary types. The secondary type, given in parentheses after the configuration block name, specifies which set of equations to solve. Note that the module settings listed under All options are available regardless of the secondary type.

Option	Description
guiding-center	Specifies the guiding-center equations of motion
particle	Specifies the particle (“full-orbit”) equations of motion

Summary of options

Option	Description
@Equation method	Numerical method used to solve equations of motion.
@Equation tolerance	Relative tolerance of ODE solver (if adaptive solver is used)

Example configuration

This example illustrates how to configure the guiding-center equations of motion:

@Equation gc (guiding-center) {
    method    = rkdp45;
    tolerance = 1e-9;
}

All options

method

Default value:rkdp45 Allowed values:rkdp45

Specifies the numerical method to use for solving the ODE that consititutes the guiding-center equations of motion. Currently, only one such numerical method is available, namely an adaptive Runge-Kutta solver of order 4, with an error estimator of order 5. The method uses Dormand-Prince coefficients, and is hence often known as the RKDP45 method [1].

tolerance

Default value:1e-9 Allowed values:\(\epsilon < \text{tolerance} < 1\)

Sets the relative tolerance to use if an adaptive ODE solver is used to solve the equations of motion. The tolerance must be smaller than one, and greater than the machine epsilon \(\epsilon\), which is \(\approx 2\cdot 10^{-16}\) using double-precision floating point numbers and \(\approx 10^{-7}\) using single-precision.

[1]	Runge-Kutta-Dormand-Prince (RKDP45), Chapter XX: Integration of differential equations, Numerical Recipes, 3rd edition.