The RungeKutta3 class provides implementations of several Runge-Kutta numerical ODE solvers. Given an unknown, time-dependent function y(t) governed by an Ordinary Differential Equation (ODE) of the form: d/dt y(t) = y'(t) = f(t, y) y(t0) = y0 Note: the integrateV method for a system of separable ODEs is mixed in from the Integrator trait. The ODE method is defined by its Extended Butcher Tablaeu (a, b, b_, c).
Value parameters
- a
-
the lower triangular matrix of constants multiplying the stage derivatives
- b
-
the vector of constants for computing the weighted average of stage derivatives
- b_
-
same for the embedded solver
- c
-
the vector of constants for shifting time
- name
-
the name the ODE solver
Attributes
- Companion
- object
- Graph
-
- Supertypes
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
-
the derivative function f(t, y) where y is a scalar
- 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
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 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
-
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
Inherited fields
The default step size for the t dimension
Estimate of the error in calculating y