Message Boards Message Boards

GROUPS:

Solve a system of Differential Equations with EigenSystem DSolve MatrixExp?

Posted 2 months ago
445 Views
|
4 Replies
|
0 Total Likes
|

In calculating a system of differential equations, I used 3 different methods: EigenSystem, DSolve and MatrixExp. DSolve and MatrixExp porduced the same answers but a different answers than EigenSystem and I don't understand why (See Attached). In all three cases, I used a default value of {1,1} for the values of the arbitrary constants. It appears that DSolve and MatrixExp simply dropped the negative exponent.

I don't understand what I am overlooking.

Thanks,

Mitch Sandlin

Attachments:
4 Replies

Hey Mitch,

Apparently there is no problem in functionality of EigenSystem - it gives the correct solution. The problem was in specified initial conditions to the EigenSystem solution. In both DSolve and MatrixExp you specified that x[0]=1 and y[0]=1, which is analogous to the following in the EigenSystem solution: enter image description here which results in {{c1 -> 0, c2 -> 1}} Thus, your final solution wont' have c1exp(1t) in it. (See attached workbook)

Attachments:

Thank you so much and I understand exactly what you are saying about actually calculating the values of c1 and c2. However I was actually trying to figure out a way to circumvent the necessity of performing the calculations for the following graphing reasons.

My ultimate goal was to use Manipulate to dynamically load the values of c1 and c2 by dragging the cursor around the graph (see bottom of attached - CalcQuestion3).

Do you have any suggestions on the best way to dynamically load the values of c1 and c2 to in conjunction with Manipulate?

Attachments:

They agree if c1 is zero...

Hi All;

Actually, my initial values are x[0]=x0 and y[0]=y0, with x0 and y0 being arbitrary initial conditions. My intention is not to find specific initial values for the constants, but to plug in values for the constants, as well as time(t) at some point in time in the future and calculate values for x and y.

There is nothing special about the values of (1,1) or (5,5) that I plugged in - they are just values that I basically picked out of thin air to test the functions to determine if they came up with the same answer. Again, it appears that DSolve and MatrixExp answers match, but EigenSystem answers do not match and I can't seem to understand why (See attachment CalcQuestion4).

I am sure that it is something that I'm overlooking, but after double and triple checking my calculations, I am still at a loss as to why the answers are different.

My ultimate goal was to use the commands: Manipulate[] along with ParametricPlot[] to dynamically load the values of the constants (initial conditions) by dragging the cursor around the graph to view the function using different constants (see bottom of attached - CalcQuestion3).

Thanks so much,

Mitch Sandlin

Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract