@Markiyan Hirnyk 

Maple provides different numerical methods for a single PDE (including methods that can handle hyperbolid PDEs in which convection dominates). Your example is a convective system and Maple's current implementation (if I am not wrong) is central difference in x and simple forward scheme in time. This is not stable for convective PDEs and hence you have this error.

That said, I have seen Maple failing even a single diffusion type PDE (linear), I will report that later. In particular, my concern was when it gave wrong numerical results (I can take a failure as in this case, but giving wrong results is dangerous).

@Joe Riel 

Is it possible to delete a file and add a modifed file (with print inserts) to the same library with the same name?

@ 

thanks

@Preben Alsholm 

It is not working in classic worksheet. thanks

@Preben Alsholm 

I suggest direct dsolve or MatrixExponential(A,t) as the general solution. A can be singular, might have complex eigenvalues, repeated eigenvalues, etc. 

Only when A has distinct eigen values, one can use the lamba,P approach

@Giulianot 

Not all DAEs can b converted to da/dt = something, db/dt = something. That is the issue.

@Giulianot 

I am glad it worked for you.

To say it short consider index 1 DAEs

dy/dt = f(y,z)

0 = g(y,z)

Maple cannot solve this DAE. It tries to convert this system to dy/dt = f(y,z) and dz/dt = g1(y,z). This is a fundamental mistake. The reason it crashed was Maple is trying to convert your system to this format and it fails. 

You are better off writing ODEs and giving consistent initial conditions. Do check my past posts which will avoid doing fsolve and might avoid tricky subsitutions (automated).

@Preben Alsholm 

Preben, yes, the objective is y2 at global time t = 1 and hence sol1(0.5) for the second stage.

Doing dsolve numeric inside the procedure obj beats the purpose. Perhaps it is still better to call once than twice.

I have tried Heaviside, tanh functions, switch functions, but no use.

Writing my own code for Hessian helps avoid this issue, but not very accurate, but atleast better than fdiff.

I think parametric dsolve numeric may not be as useful as I thought it would be. When inconsistent results are obtained, this concerns me a lot. Proper testing has not been done for these procedures and commands.

in fact, I am not able to get classic maple worksheet to work in windows 10 in most of my computers or laptops. Some of my students are lucky, it works for them. Maple installs fine, but nothing can be saved. When you run Maple, it will crash.

I even wiped out 10, reinstalled still no luck.

In just one of my new laptops (1 out of 10 computers/laptops in my group), I reinstalled windows 10, within 10 minutes installed Maple  14 (before even it went online for updates), it works without crashing. For some weird reasons, any future installations (Maple 18, 2015, 2016) has the same problem of crashing (classic worksheet crashes). 

However mw format works fine. This is unfortunate

@Carl Love 

I was just trying to correct the statement made by OP (sorry, I jump in whenever inaccurate statements are made. This includes current help files for dsolve numeric which already has some mistakes and wrong claims. I don't want an ignorant person to wrongly add this into future help files). We can't get the exact time steps used by dsolve numeric unless a procedure is used. This is actually very limiting as I am not sure how to do this is in compiled form for efficiency (I need to know the exact time steps some times).

We can agree that plot, implicitplot or odeplot, all of them just choose points based on quality of plots (guaranteeing error tolerance) not the stiffness of the original model (or time steps).

@sand 15

The commands you give don't seem to pick the time steps chosen by dsolve (adaptive time stepping). For test problems, it seems to pick 201 data points (0 to 1 for the model dy/dt = -y, dy/dt =-y^2, etc). The output you get will be just that.

If you want Maple's dsolve numeric adaptive time steps, you need to define the model as a procedure (function) and make Maple print the values of t for the time steps. for example. please check the procedure I used in

http://www.mapleprimes.com/posts/204894-Please-Bring-Back-Dsolve-Numeric-Method--Mgear

@Carl Love 

That helps a lot. I am not aware of the shortcuts. I was under the impression that shortcuts are just for typing convenience and not for efficiency in calculation or reduction in RAM. If that changes, let me know.

@Carl Love 

Your approach seems to be good. Can you please be kind enough to minimize using shortcuts for the commands and codes and split your commands as multiple lines?

Thanks

For example I would like see as OP posted

a:=[];

and then step by step commands to arrive at your final answer. thanks.

I am trying to figure what x[2], x[1] mean in your command

@taro 

more than 5 minutes to just open in mw format. opens in less than a second in mws format.

It may not be Java, but perhaps the added bells and whistles in Java format.

@ 

I hear from my staff's recent interaction with Maplesoft folks that Maple is moving away from Java based GUI and interface.  I sincerely hope that they will try to arrive at a gui very close to the previous classic mws interface.