Numwrical integration

[nvsuryan]

I numerically integrated a non-linear two-point boundary layer problem using Mathcad 11 and Mathcad 15. The two give slightly different values with Mathcad 11 producing a more plausible result. Anyone knows the reason for the difference?

[AlanStevens]

Can't tell without seeing the worksheets. Upload them.

Alan

[nvsuryan]

The attached file shows the actual programming

As I said before the difference is small but it bothered me that the same software should give slightly different results.

[PhilipOakley]

As I remember it the default integration method has changed between V11 and V15, so slight variation can come from that.

In addition it is easily possible to badly formulate the equation being integrated, such that the algorithm doesn't find (when searching for high points in the graph) the area under the curve - this is particularly true for graphs that are shown on a log-log scale in text books, which are simply a spike on a lin-lin plot (i.e. as seen by the numeric integral). I'd expect PDE/ODEs to have a problem with this some times.

As said by Alan, at least post an example sheet that extracts the issue you are demonstrating.

[nvsuryan]

I again compared the results of numerical intgration in thwo versions with identical boundary conditions. Thre is a slight difference in the results, which, I think are caused by the default items in the two versions.

But the differences are small and not worth pursuing any further.

Thanks for helping me out.

[MikeArmstrong]

Again no example. This thread is pointless without examples to work with.

[nvsuryan]

The attached file shows the actual programming

As I said before the difference is small but it bothered me that the same software should give slightly different results.

[nvsuryan]

The attached file shows the actual programming

As I said before the difference is small but it bothered me that the same software should give slightly different results.

[AlanStevens]

The default solver in M15 is different from that in M11. You can easily change your results in M15 simply by selecting another solver (right-click on Odesolve to choose). If you have the default tolerance set (10^-3), then both values are correct to within this of course!.

Also, you might find it more convenient to solve this sort of problem as follows, rather than creating two solve blocks:

Alan

[Werner_E]

Why don't you attach the actual sheets?

I am not surprised about those small differences in the numeric results of MC11 and MC15. There sure were some modifications made concerning the numeric algorithms implemented.

Some remarks about the way you derive the value for y"(0) and the derivatives of your function:

1) You may find the optimal value for y"(0) using a solve block with find

2) If the only reason for the two additional odesolve blocks with z and h is to get the first and second derivative of your function y you should consider that you can apply Mathcads derivative operator even on "functions" created by odesolve. So there is no need for those solve blocks:

Find attached a sheet in MC15 format.