RungeKutta
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.
Attributes
- Graph
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- Supertypes
- Self type
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RungeKutta.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 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
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the derivative function f(t, y) where y is a scalar
- step
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the step size
- t
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the time value at which to compute y(t)
- t0
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the initial time
- y0
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the 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 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
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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
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the initial value vector, y0 = y(t0)
Attributes
- Inherited from:
- Integrator
Inherited fields
The default step size for the t dimension
Estimate of the error in calculating y