MATSLISE: Eigenvalues window    

The Eigenvalues window

The Eigenvalues-window allows the user to calculate the eigenvalues of the problem he/she specified.

Figure 5: The eigenvalues-window for the Harmonic Oscillator.

The Eigenvalues window: the Input-frame

In the Input-frame there is a choice between two radio-buttons:

Indices between...and...

The user enters a lower and upper index. The eigenvalues with index between this lower and upper index will be calculated. One single eigenvalue is calculated when the upper index is equal to the lower index. The eigenvalues are indexed from 0, not 1.

Eigenvalues between...and...

The user specifies the lower and upper limits of the interval to be scanned for eigenvalues, e.g. when the user wants to calculate the eigenvalues larger than zero and smaller than twenty, he enters 0 and 20 in the two inputfields.


Pressing the Calculate Eigenvalues-button starts the computations, which can be interrupted by clicking the Stop-button.


The Eigenvalues window: The Results frame

Pressing the Calculate Eigenvalues-button calculates the eigenvalues and displays them in the Results-frame. The estimated errors are also displayed. This estimated error is not the same as the real error. The eigenvalues are calculated using the CPM{16,14} and on a partition which has stepsizes consistent with the accuracy requested by the user in the results produced on this partition. To construct an estimation of the error in these eigenvalues, the eigenvalues are recalculated on the same partition but using the higher order CPM{18,16}. The difference between the CPM{18,16}-eigenvalues and the CPM{16,14}-eigenvalues forms then an estimation of the error in the CPM{16,14}-eigenvalues.
When the calculation of a certain eigenvalue did not succeed an error message is displayed and a NOK-label indicates the incorrect eigenvalues in the results-list. This may suggest that the input tolerance should be decreased or that the eigenvalues are so close that the double precision arithmetic is not sufficient to differentiate between the eigenvalues adequately.

The Plot-button

The eigenvalues displayed in the Results-frame can be visualized. In order to do this, the user must first select the eigenvalues to plot and then press the Plot-button. It is possible to select all the eigenvalues by using the Select All-button. Specific eigenvalues in the list are selected by using the SHIFT- and CTRL-keys. Two plots are constructed:

The Eigenfunction-button

The eigenfunctions associated to the selected eigenvalues are calculated by pressing the Eigenfunction-button, which opens a new window. When only one eigenvalue is selected the Eigenfunction window is opened; when more than one eigenvalue is selected another window is opened: the Eigenfunctions window.

The Workspace button

It may be useful to assign the obtained values to workspace variables (e.g. for subsequent manipulation). The Workspace-button creates a input dialog box where the user should specify variable-names for the indices, the eigenvalues and the errors of the selected entries in the list. These values become then available in the base-workspace under the specified names.


The Eigenvalues window: The Menu

File: Print

prints the Eigenvalues window

File: Close

closes the Eigenvalues window

Edit: Copy results to clipboard

copies the results to the clipboard

Help: Help on "eigenvalues"

displays the helpfile for the Eigenvalues-window

Help: MATSLISE:help

displays the helpfiles for the MATSLISE-application

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