| Author | Message | ||
     Mohammad Rahmani (mrahmani) Member Username: mrahmani Post Number: 17 Registered: 10-2004 |
There is an example in FlexPDE sample folder called tintegral.PDE ( FlexPDE4\Samples\misc\tintegral.pde). A history plot shows the the values of " tintegral(1) " which is equal to "t". Considering the interval of integration (-0.5 to 19) you expect a linear graph but if you look at the output you will see the value is 0 at t=-0.5 and the final value is (19.25) for t=19. For clarity you can export the result to a file as follows: history(t1) as "Tintegral(1)" export format "#t#b#1" File="Tint.txt" and you will see the following values. ------------------------------------------------------------- FlexPDE Version 4.2.4 12:54:26 Nov 17 2004 tintegral-R0.pde 11:25:41 12/5/04 Title: Tintegral(1) Time 19 } -0.5000000000 0. -0.4998313120 -0.2496626239 -0.4996626239 -0.2496626239 -0.4994939359 -0.2494939359 -0.4992577727 -0.2492577727 -0.4989271441 -0.2489271441 ...................... ...................... 18.500000000 18.75 18.602938913 18.852938913 18.705877827 18.955877827 18.808816740 19.05881674 18.911755653 19.161755653 19.000000000 19.25 Is it because "t" should start from 0 or there is another reason? /Mohammad | ||
| Mongi Mansouri (mongim_pde) Member Username: mongim_pde Post Number: 31 Registered: 11-2003 |
Mohammad, U're right. I think this is a glitch that needs to be fixed. I tried the same sample with the below lines added, and its gives the expected result for t2. It seems that if u dont fix time step, it does not compute the integral correctly. In addition, without the if-statement, the initial value of the integration is always wrong but all other value are correct. Hope this will shed some light as to the problem and how to fix it. /Mongi Here are the lines I added to the sample pde: select fixdt !! this goes before variable declaration. definitions .......................... t0=-0.5; tf=19; tstep=0.5; t1 = time_integral(1.0); !! t1 has error at initial point. t2 = if(t>t0) then time_integral(1.0) else t0; !! t2 gives correct integral. .............. time t0 to tf by tstep histories history(t1, t2) as "Tintegral(1)" export format "#t #1 #2" File="Tint.txt" | ||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 273 Registered: 06-2003 |
FlexPDE uses a two-step integration method in time. This requires that the first timestep be treated specially. Apparently there is an error in computation of the tintegral over the first timestep if the start time is not zero. (Probably the code assumes a zero start time.) I will correct this in the next maintenance release. In the meantime, you can cure the problem by starting at time=0. | ||
| Mohammad Rahmani (mrahmani) Member Username: mrahmani Post Number: 18 Registered: 10-2004 |
Thanks to both you Mongi and Robert. The method Mongi has proposed cure the first ouput but remains for later time points. Of course by strating from 0 the result are correct. /Mohammad |