DormandPrince
The DormandPrince object 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 form d/dt y(t) = f(t, y) compute y(t) using a (4,5)-order Dormand-Prince Integrator (DOPRI) or ode45. Note: the integrateV method for a system of separable ODEs is mixed in from the Integrator trait.
Attributes
- See also
- Graph
-
- Supertypes
- Self type
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DormandPrince.type
Members list
Value members
Concrete methods
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.
Value parameters
- f
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the derivative function f(t, y)
- step
-
the middle step size
- t
-
the time value at which to compute y(t)
- t0
-
the initial time
- y0
-
value of the y-function at time t0, y0 = y(t0)
Attributes
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.
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.
Value parameters
- f
-
the derivative function f(t, y)
- hmax
-
the maximum step size
- hmin
-
the minimum step size
- maxSteps
-
the maximum number of steps
- t
-
the time value at which to compute y(t)
- t0
-
the initial time
- tol
-
the tolerance
- y0
-
value of the y-function at time t0, y0 = y(t0)
Attributes
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.
Value parameters
- f
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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)
Attributes
Inherited methods
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. 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).
Value parameters
- f
-
the array of derivative functions [f_j(t, y_j)]
- step
-
the step size
- t
-
the time value at which to compute y(t)
- t0
-
the initial time
- y0
-
the initial value vector, y0 = y(t0)
Attributes
- Inherited from:
- Integrator
Concrete fields
Butcher tableau @see http://en.wikipedia.org/wiki/Dormand–Prince_method
Inherited fields
The default step size for the t dimension
Estimate of the error in calculating y