@Carl Love 

At this instance, I'm sure that the matrice is sparse. When the storage is not defined sparse, the PC is bloked.

More time is necessary for me to define exactly the patern and other characteritics of the matrice.

My initial goal, is how to solve the sparse matrice using SparseDirect where the precision is better than SparceIterative.

Thanks

@Carl Love 

I do a replay, but I cannot see it here ?

I explained in my comment not published here that my matrice is globaly band with few values not in the band. The storage band cannot be used.

I'm not ignoring the answer but I'm still searching for the solution in solving my system using Maple or I shoud use another software.

 Dr. Venkat gives an interesting comment in relation with sparse matrix not really band.

I see his code, but if he can gives an example how to use it to solve a system, I can use it without difficulties.

Thanks

@ 

Thank you, I must study the code for utilisation in my case.

@Carl Love 

With adding datatype= hfloat and Digits:=15, the memory is lesser but LinearSolve(A,B) gives the norm of the residual 2.5e+7. I use also sparse storage.

When using SparseDirect my PC is Blocked.

@ 

Thank you for your answer.

I consulted the link and it is very interesting. I must solve this type of matrix many times.

Yes, I'm thinking to use vector format to replace the matrix with vectors. In this case, I must use my own solver. LinearSolve doesnt use vectors.

Befor this, I'm searching for other possibilities with using LinearSolve.

@Carl Love 

Thank you for your answer.

Yes the matrix is banded on tridiagonal. I have difficulty to give sparsematrixplot.

@acer 

The proposed way is ok for me.

I noticed your given comments. 

@ 

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. dae.mw

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.

dae.mw

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.

@acer 

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.

Thanks