The RungeKutta object provides an implementation of a classical numerical ODE solver. Given an unknown, time-dependent function y(t) governed by an Ordinary Differential Equation (ODE) of the form: d/dt y(t) = f(t, y) Compute y(t) using a 4th-order Runge-Kutta Integrator (RK4). Note: the 'integrateV' method for a system of separable ODEs is mixed in from the Integrator trait.
Compute y(t) governed by a differential equation using numerical integration of the derivative function f(t, y) using a 4th-order Runge-Kutta method to return the value of y(t) at time t.
Compute y(t) governed by a differential equation using numerical integration of the derivative function f(t, y) using a 4th-order Runge-Kutta method to return the value of y(t) at time t.
Value parameters
f
the derivative function f(t, y) where y is a scalar
step
the step size
t
the time value at which to compute y(t)
t0
the initial time
y0
the value of the y-function at time t0, y0 = y(t0)
Compute y(t), a vector, governed by a system of differential equations using numerical integration of the derivative function f(t, y) using a 4th-order Runge-Kutta method to return the value of y(t) at time t.
Compute y(t), a vector, governed by a system of differential equations using numerical integration of the derivative function f(t, y) using a 4th-order Runge-Kutta method to return the value of y(t) at time t.
Value parameters
f
the array of derivative functions [f(t, y)] where y is a vector
step
the step size
t
the time value at which to compute y(t)
t0
the initial time
y0
the value of the y-function at time t0, y0 = y(t0)
Apply the integrate method to each derivative to compute the trajectory of a time-dependent vector function y(t) governed by a separable system of Ordinary Differential Equations (ODE's) where [f_j(t, y_j)] is an array of derivative functions. Each derivative function takes a scalar t and a scalar y_j = y(j).
Apply the integrate method to each derivative to compute the trajectory of a time-dependent vector function y(t) governed by a separable system of Ordinary Differential Equations (ODE's) where [f_j(t, y_j)] is an array of derivative functions. Each derivative function takes a scalar t and a scalar y_j = y(j).