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These are replies submitted by Alger


Thank you for your work. I will try to understand and apply to my models.

Although, my models seems to be complicated to be considered as DAE. Considering known functions of the model as variable having initial condition can be difficult physically.

Thanks again

@Preben Alsholm 

Yes, when C<=35e-6 (perhaps 40e-6), all the variables are zero at t=infinity, i.e. ids, vds, idr, vds, etc...

When, C>=35e-6 (perhaps 40e-6), the variables tend to be not null. When C is high, i.e. C>70e-6 or higher, the range where the variables are different to zero is small. When 35e-6<=C<=45e-6, the range where the variables are diffrent from zero should be high.


@Preben Alsholm 

I telecharged your worksheet and it is very optimized. Thank you.

Although, the problem of range and singularity exist when I change the parameter C and range. Variables of the model should be null when C<40e-6 and can be not null when C>40e-6 with imposing high range.

I read Maple help and I found that the DAE can solve systems of ODE for high range without writing the system as dy/dt = f.

The problem is how to re-write the system with the existing of piecewise functions, add them as niew variables and solve the system of ODE using DAE.

I don't know if DAE is a good idea, but I think it is the only solution for problem of range and singularity.

I posted a simplified example of the system with less piecewise functions if it can be re-written as DAE.

Thank you  


I simplified the problem and I write it as classic worksheet to understand how to solve a system of ODE using DAE.

Find in the attached file the exemple.

If it is possible de solve the system without dy/dt = f it is very interesting. Also, I don't know how eliminate my piecewise functions for adding them as variables.

Thank you in advance


Thank you for your propositions. However, I have not experience in DAE and I don't know how to modify the system to add other variables.

I will work on it.


@Preben Alsholm 

Thank you very much for your work and your help.

I know that the solution exist for C>=40e-6 and can be zero for C<=35e-6. I'm not anso convainced that there is a singularity for C=50e-6.

Thank you again

@Preben Alsholm 

Thank you, perhaps I should take a look on my model.


Thank you, with your propositions dsolve take less time and the plots are better especially when the plot is done with odeplot as proposed bu Preben Alsholm 11499 .

I changed the parameter C=45e-6 and the range to 0-100s. dsolve give me this warning:

Warning, cannot evaluate the solution further right of 53.938333, probably a singularity
Why, there is not a singularity.



Thank you

@Carl Love 

Yes, this storage take little memory. There is no need to work with vectors.

Thank you very much.


I have big Matrix(150000,150000) which consume high memory.

I think store the matrix as vectors representing the diagonal and non zero values is good idea.

How to use vectors instead matrix and solve the system for very big matrices

@Carl Love 

When I initialize the matrix with Matrix(150000, 150000) and work with it, the consumed memory is very high.

For this, I want to store the matrix as vectors and solve the system. The vectors are corresponding to non zero values and ther positions in row and colon.



Your answer is very helpfull and I must read and develop your proposition.

Thank you 


Thank you very much for your response which is very helpfull.

Although, how to know the values of A(i) by seeing the different colors of the 3d curve.

Is it possible to get with the plot a bar graphe (or legend) where there are all the colors of the plot with an indication of the values of colors.



Thank you for the answer.

I attached a part of my code.

Replacing A with color is a good idea for a plot equivalent to density plot.


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