High-order nonlinear solver for multiple roots

A method of order four for finding multiple zeros of nonlinear functions is developed. The method is based on Jarratt’s 4 fifth-order method (for simple roots) and it requires one evaluation of the function and three evaluations of the derivative. The 5 informational efficiency of the method is the same as previously developed schemes of lower order. For the special case of double 6 root, we found a family of fourth-order methods requiring one less derivative. Thus this family is more efficient than all others. All 7 these methods require the knowledge of the multiplicity. 8 c © 2007 Published by Elsevier Ltd 9