Table Of Contents
ODE Solver (VI) (G Dataflow)
Solves ordinary differential equations that you define with a strictly typed VI reference.
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ODE
Strictly typed reference to the VI that implements the ordinary differential equation.
initial values
Vector of the initial values of the variables.
The components of initial values correspond to the components of x.
simulation parameters
Set of parameters to configure the numerical solution of the differential equations.
initial time
Start time for solving the differential equations.
final time
End time for solving the differential equations. final time must be greater than initial time.
continuous solver
Type of solver this node uses to solve the differential equations.
| Name | Value | Description |
|---|---|---|
| Runge-Kutta 1 (Euler) | 0 | A fixed step-size, single-step solver of first order. This solver applies to ODEs only. |
| Runge-Kutta 2 | 1 | A fixed step-size, single-step solver of second order. This solver applies to ODEs only. |
| Runge-Kutta 3 | 2 | A fixed step-size, single-step solver of third order. This solver applies to ODEs only. |
| Runge-Kutta 4 | 3 | A fixed step-size, single-step solver of fourth order. This solver applies to ODEs only. |
| Runge-Kutta 23 (Variable) | 4 | A variable step-size solver that starts with a third order method and embeds a set of Bogacki-Shampine coefficients for a second order method. This solver applies to ODEs only. |
| Runge-Kutta 45 (Variable) | 5 | A variable step-size solver that starts with a fifth order method and embeds a set of Dormand-Prince coefficients for a fourth order method. This solver applies to ODEs only. |
| BDF (Variable) | 6 | A variable step-size, variable order (orders 1 through 5) implementation of the multi-step backwards differentiation formula (BDF). This method is suitable for moderately stiff problems. |
| Adams-Moulton (Variable) | 7 | A variable step-size, multi-step variable order (orders 1 through 12) implementation of the Adams-Moulton predictor-corrector pair in predict-evaluate-correct-evaluate (PECE) mode. This solver provides efficient and accurate solutions for non-stiff ODEs. |
| Rosenbrock (Variable) | 8 | A variable step-size, single-step explicit solver that uses a second order method with third order error estimates. This solver applies to ODEs only. |
| Discrete States Only | 9 | Fixed step-size, single-step algorithm for simulations that contain no continuous functions and therefore no differential equations. This solver applies to ODEs only. |
| SDIRK4 (Variable) | 10 | A variable step-size solver of the fourth order. This solver is a singly diagonal implicit Runge-Kutta method (SDIRK). This solver applies to ODEs only. |
| Radau 5 (Variable) | 11 | A variable step-size Radau solver of the fifth order. |
| Radau 9 (Variable) | 12 | A variable step-size Radau solver of the ninth order. |
| Radau 13 (Variable) | 13 | A variable step-size Radau solver of the thirteenth order. |
| Radau [Variable Order] (Variable) | 14 | A variable step-size Radau solver of variable order. |
| Gear's Method (Variable) | 15 | A variable step-size, variable order solver that implements a multi-step BDF. This solver is efficient for stiff problems and suitable for DAEs with implicit linear and nonlinear algebraic constraints. |
time step
Interval, in seconds, between the times at which this node evaluates the model and updates the model output. The node uses this input only if you select a fixed step-size solver.
initial time step
Step size for the first time step that the solver uses to solve the differential equations. The node uses this input only if you select a variable step-size solver.
minimum time step
Smallest time step size that the solver can use to solve the differential equations. The node uses this input only if you select a variable step-size solver.
maximum time step
Largest time step size that the solver can use to solve the differential equations. The node uses this input only if you select a variable step-size solver.
absolute tolerance
Absolute tolerance the solver uses to control the local error for each variable.
You must specify a scalar tolerance which applies to all variables. absolute tolerance cannot be negative. The corresponding absolute tolerance and relative tolerance cannot both be zeroes.
relative tolerance
Relative tolerance the solver uses to control the local error for each variable state.
You must specify a scalar tolerance which applies to all variables. relative tolerance cannot be negative. The corresponding absolute tolerance and relative tolerance cannot both be zeroes.
discrete time step
Base time step, in seconds, to use for discrete functions.
This input is used only for the ODE solver.
If you select a fixed step-size solver, discrete time step must be an integer multiple of time step. Otherwise, a run-time error occurs when you attempt to run the simulation.
data
Arbitrary values passed to the strictly typed VI reference.
error in
Error conditions that occur before this node runs.
The node responds to this input according to standard error behavior.
Standard Error Behavior
Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.
Default: No error
times
Points of time at which the differential equation solver evaluates the state.
If you select a fixed step-size solver, the values in times are evenly spaced.
x
Values of the variables over time.
Each row of x contains the values evaluated at a particular time and each column contains a history of a particular value over time.
error out
Error information.
The node produces this output according to standard error behavior.
Standard Error Behavior
Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.
Controlling the Local Error
The solver calculates the local error by the following equation: |x| * relative tolerance + absolute tolerance.
This node uses this error to adjust the step size. If the error is too large, the solver rejects the current step and reduces the step size for another try. If the error is too small, the solver accepts the current step and increases the step size for next try. The relative tolerance has greater impact on the local error when x is relatively large. The absolute tolerance has greater impact on the local error when x is relatively small.
Where This Node Can Run:
Desktop OS: Windows
FPGA: Not supported
Web Server: Not supported in VIs that run in a web application