Butcher tableau @see http://en.
Butcher tableau @see http://en.wikipedia.org/wiki/Dormand–Prince_method
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 (4,5)-order Dormand-Prince 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 (4,5)-order Dormand-Prince method to return the value of y(t) at time t.
the derivative function f(t, y)
value of the y-function at time t0, y0 = y(t0)
the time value at which to compute y(t)
the initial time
the middle step size
Compute y(t) governed by a differential equation using numerical integration of the derivative function f(t, y) using a (4,5)-order Dormand-Prince 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 (4,5)-order Dormand-Prince method to return the value of y(t) at time t. The method provides more customization options.
the derivative function f(t, y)
value of the y-function at time t0, y0 = y(t0)
the time value at which to compute y(t)
the minimum step size
the maximum step size
the initial time
the tolerance
the maximum number of steps
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 (4,5)-order Dormand-Prince 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 (4,5)-order Dormand-Prince 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
DormandPrinceobject provides a state-of-the-art numerical ODE solver. Given an unknown, time-dependent function 'y(t)' governed by an Ordinary Differential Equation (ODE) of the formd/dt y(t) = f(t, y)
compute 'y(t)' using a (4,5)-order Dormand-Prince Integrator (DOPRI). Note: the integrateV method for a system of separable ODEs is mixed in from the Integrator trait.
http://adorio-research.org/wordpress/?p=6565