Solves an n-dimension, homogeneous linear system of differential equations with solutions in numeric form.
An n-by-n matrix that describes the linear system.
Requirements for Input Matrices
This node works properly for almost all cases of real matrices that have repeated eigenvalues, complex conjugate eigenvalues, and so on. The exception is the case of a singular eigenvector matrix, that is, a matrix in which the eigenvectors do not span the whole space. If the eigenvector matrix is singular, this node returns an error of -23016.
Vector of the initial values of the variables.
The components of initial values corresponds to the components of x.
Start time for solving the differential equations.
Default: 0
End time for solving the differential equations.
Default: 1
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
Interval, in seconds, between the times at which this node evaluates the model and updates the model output.
Default: 0.1
Points of time at which the node solves the differential equations. The method yields equidistant time steps between start time and end time.
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 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.
Linear systems can be described by
where
This node solves the linear system by the determination of the eigenvalues and eigenvectors of A. Let S be the set of all eigenvectors spanning the whole n-dimensional space. The transformation y(t) = Sx(t) yields:
The matrix SAS^{-1} has diagonal form. The solution x(t) can be determined by back-transformation: x(t) = S^{-1}y(t).
To solve the following system of linear differential equations:
with x_{1}(0) = 1, x_{2}(0) = 2, x_{3}(0) = 3, and x_{4}(0) = 4.
Enter the following values:
The solution of this equation is as follows:
The following illustration shows the four components of the solution of the linear differential equation:
Where This Node Can Run:
Desktop OS: Windows
FPGA: This product does not support FPGA devices