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.