A comparison of the Newton-Krylov method with high order Newton-like methods to solve nonlinear systems

We compare the CPU time and error estimates of some variants of Newton method of the third and fourth-order convergence with those of the Newton-Krylov method used to solve systems of nonlinear equations. By expanding some numerical experiments we show that the use of Newton-Krylov method is better in the cost and accuracy points of view than the use of other high order Newton-like methods when the system is sparse and its size is large.