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Some modified Newton’s methods withfourth-order convergence

J. R. Sharmaa, R. K. Guhaa and Rajni Sharma

Based on Newton method, we derive three efficient methods of order four for solving nonlinear equations. Per iteration each method requires three evaluations and therefore the efficiency index of the methods is 1.587 which is better than Newton’s efficiency index 1.414. Performance of the methods is compared with closest competitors in a series of numerical examples.It is shown by way of illustration these methods are very useful in the applications requiring high precision in computations. Moreover, theoretical order of convergence is verified on the examples.