Numerical Recipes http://numerical.recipes/

SciPy Python-based open-source software https://www.scipy.org/

GNU Octave https://www.gnu.org/software/octave/

and, last but not least, Matlab

plus, a plenitude more free and commercial tools are on the market

Thank you Michael Zakharov .

I suggest Matlab and Maple, each one havig specific features for numerical analysis problems.

If you use Fortran or C++ you should find suitable libraries.

Thank you Filippo Maria Denaro

In addition to the other good recommendations, I would include 'R'. It is a great numerical platform with excellent graphics capability and can be downloaded from:

https://www.r-project.org/

R has numerous free numerical and plotting packages for many different applications, see:

https://cran.r-project.org/web/packages/available_packages_by_date.html

R is an open source free computing system that, when combined with the 'RStudio' GUI interface, provides an excellent computing platform. RSTudio can be downloaded from:

https://www.rstudio.com/

A search on YouTube will bring up many R tutorials.

Good luck with your search.

@M.I.Afjal

My suggestion is that use MATLAB .

With a little effort you can do it. However

cross check with known analytical results.

Good luck

B.Rath

Mathematica by Wolfram. I made that choice decades ago and never regretted it.

That seems to me too broad. Be a bit more specific. Computing what? And what are the methods u whish to use to make the computation ?

For general purpose. Actually for undergraduate lab/practical course "Numerical analysis for engineers".

Originally, I was use matlab and mathematica occasionally for this types of work but want to know some package program/tools for specifically numerical analysis work. such as Interpolation, regression, differentiations, integration, partial differentiation, ordinary 1st order, 2nd order partial differentiation, solving linear non linear equation etc (methods: newton, rungi-kurtha, euler, raphsion and so others) @Chama.

Thanks all for your answer. I think, I got my answer.

These are exactly the type of problems i used to assist one professor at uct. We use matlab. We familiarise the students with both build-in function, such as ode45, and also write down their own code. So i thing u need software that has advanced buiild in function and that can also allow the students to edit their own program.

Thank you again@ Chama

Matlab

If your budget does not allow MATLAB or MAPLE, I would suggest Octave or Scilab intead of Matlab and Maxima instead of Maple/

Thank you @ Jos J van Kan

Many excellent options have been already mentioned. I would like to add SageMath:

https://www.sagemath.org/

SageMath is a free open-source mathematics software system licensed under the GPL. It builds on top of many existing open-source packages: NumPy, SciPy, matplotlib,Sympy, Maxima, GAP, FLINT, R and many more. With SageMath you can access their combined power through a common, Python-based language or directly via interfaces or wrappers.

SageMath mission is to create a viable free open source alternative to Magma, Maple, Mathematica and Matlab.

Thank you @Manuele Santoprete

Masud Ibn Afjal , for some of problems you cited above, we have a C++ library called Trilinos (https://trilinos.org/). If you want to implement your own program and if you would like to work with large problems, you can use it.

Another option is MATLAB. It has an easy language and lots of numerical analysis tools (or Octave, if you don' t have access to a Matlab license).

For symbolic languages, I suggest you Maple and Mathematica. You can use symbolic language in MATLAB too, but I think Maple and Mathematica are better.

Thank you Dr. Virginia Costa

Some of the most used software for numerical computations are MATLAB and MAPLE

For PDEs, Freefem++ .

Very good.

what matlab code do you need

MATLAB is extremely good for numerical simulations and computations.

MATLAB or Python is a good option.