# Difference between NSolve and FindRoot?

While it is clear what FindRoot does (start at a point and look for local extremum using gradient), how does NSolve work?

Also, could anyone share a summary of all the Mathematica commands to solve nonlinear systems of equations?

• Try searching the docs for equation solving. – Michael E2 Oct 30 '18 at 16:18
• I found that: "NSolve is a global equation solver" and "FindRoot is a local equation solver". Does it mean that FindRoot is satisfied as soon as it finds a solution, while NSolve keeps looking? In other words, FindRoot is an Nsolve that looks around the initial value and stops at the first solution. Correct? – Tecon Oct 30 '18 at 16:28
• Yes about FindRoot. I would say that NSolve tries to find all roots. (I say "tries" because there are computational limits.) Originally it was primarily a polynomial equation solver, but it has expanded its bag of tricks (esp. for univariate equations). – Michael E2 Oct 30 '18 at 16:37
• Ok, thank you very much. – Tecon Oct 30 '18 at 16:46