I have a set of non-linear equations that I want to solve numerically. The "Solver" of Excel is sometimes able to solve it, but often fails (ends up with not-a-number values and gives up).
I am thinking of switching to Mathematica or Matlab. Would appreciate if someone gave me any guidance about the pros and cons of these two.
I suggest you get a trial version of each and test them out on your problem.
Checking on trial versions per suggestion by @FrankKampas is a very good idea. Also you might want to post some sample equation sets, if you want advice from the forum on solver capabilities or methods to use (very hard to provide such in the absence of examples).
I agree with Frank and Daniel but also have some general comments. I use both products extensively but since this is a Mathematica forum I will only discuss Mathematica. They are good for different things. Mathematica has a "notebook" structure which is particularly good for maintaining a record of the derivation of your equations. It is also good for keeping a record of starting conditions, results, plots, data, and general comments and documentation. You can even paste images in the notebooks and interact with your notebook dynamically. I find the Mathematica notebooks replace paper so I do not lose or misplace my work. I hope this helps.