The default step size for the t dimension
The default step size for the t dimension
Estimate of the error in calculating y
Estimate of the error in calculating y
Show the flaw by printing the error message.
Show the flaw by printing the error message.
the method where the error occurred
the error message
Get the error estimate.
Get the error estimate.
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.
the derivative function f(t, y) where y is a scalar
the value of the y-function at time t0, y0 = y(t0)
the time value at which to compute y(t)
the initial time
the step size
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.
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).
the array of derivative functions [f_j(t, y_j)]
the initial value vector, y0 = y(t0)
the time value at which to compute y(t)
the initial time
the step size
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.
the array of derivative functions [f(t, y)] where y is a vector
the value of the y-function at time t0, y0 = y(t0)
the time value at which to compute y(t)
the initial time
the step size
The
RungeKuttaobject 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.