Use numerical integration to compute the trajectory of an unknown, time- dependent function y(t) governed by a first-order ODE of the form y(t)' = f(t, y), i.
Use numerical integration to compute the trajectory of an unknown, time- dependent function y(t) governed by a first-order ODE of the form y(t)' = f(t, y), i.e., the time derivative of y(t) equals f(t, y). The derivative function f(t, y) is integrated using a numerical integrator (e.g., Runge-Kutta) to return the value of y(t) at time t. The derivative function takes a scalar t and a scalar y.
the derivative function f(t, y)
the intial 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
Use numerical integration to compute the trajectory of an unknown, time- dependent vector function y(t) governed by a system of first-order ODEs of the form y(t)' = f(t, y).
Use numerical integration to compute the trajectory of an unknown, time- dependent vector function y(t) governed by a system of first-order ODEs of the form y(t)' = f(t, y). The j-th derivative in the array of derivative functions, [f_j(t, y)], takes a scalar t and a vector y (note the other integrate methods take a scalar t and a scalar y.
the array of derivative functions [f_j(t, y)]
the initial value vector, y0 = y(t0)
the time value at which to compute y(t)
the initial time
the step size
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.
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
The
Integratortrait provides a template for writing numerical integrators (e.g., Runge-Kutta (RK4) or Dormand-Prince (DOPRI)) to produce trajectories for first-order Ordinary Differential Equations (ODE's). The ODE is of the form:d/dt y(t) = f(t, y) with initial condition y0 = y(t0)
If 'f' is a linear function of the form 'a(t) * y(t) + b(t)', then the ODE is linear, if 'a(t) = a' (i.e., a constant) the ODE has constant coefficients and if 'b(t) = 0' the ODE is homogeneous. Note this package provides a solver (not an integrator) as an option for linear, constant coefficient, homogeneous, first-order ODE.
scalation.dynamics.LinearDiffEq.scala