New predictor–corrector methods of second-order for solving nonlinear equations

References

• Chen , J. H. 2007 . New modified regula falsi method for nonlinear equations . Appl. Math. Comput. , 184 : 965 – 971 .
   Web of Science ®Google Scholar
• Chen , J. H. and Li , W. G. 2007 . An improved exponential regula falsi methods with quadratic convergence of both diameter and point for solving nonlinear equations . Appl. Numer. Math. , 57 : p80 – 88 .
   Web of Science ®Google Scholar
• Chen , J. H. and Shen , Z. H. 2007 . On third-order convergent regula falsi method . Appl. Math. Comput. , 188 : 1592 – 1596 .
   Web of Science ®Google Scholar
• Chun , C. 2007 . A geometric construction of iterative functions of order three to solve nonlinear equations . Comput. Math. Appl. , 53 : 972 – 976 .
   Web of Science ®Google Scholar
• Chun , C. 2008 . A simply contructed third-order modification of Newton's method . J. Comput. Appl. Math. , 219 : 81 – 89 .
   Web of Science ®Google Scholar
• Chun , C. and Neta , B. 2008 . Some modification of Newtons method by the method of undetermined coefficients . Comput. Math. Appl. , 56 : 2528 – 2538 .
   Web of Science ®Google Scholar
• Cordero , A. and Torregrosa , J. R. 2008 . A class of multi-point iterative methods for nonlinear equations . Appl. Math. Comput. , 197 : 337 – 344 .
   Web of Science ®Google Scholar
• Feng , X. L. and He , Y. N. 2006 . Parametric iterative methods of second-order for solving nonlinear equation . Appl. Math. Comput. , 173 : 1060 – 1067 .
   Web of Science ®Google Scholar
• Feng , X. L. and He , Y. N. 2007 . High order iterative methods without derivatives for solving nonlinear equations . Appl. Math. Comput. , 186 : 1617 – 1623 .
   Web of Science ®Google Scholar
• Kanwar , M. V. , Kukreja , V. K. and Singh , S. 2005 . On some third-order iterative methods for solving nonlinear equations . Appl. Math. Comput. , 171 : 272 – 280 .
   Web of Science ®Google Scholar
• King , R. F. 1971 . A fifth-order family of modified Newton methods . BIT , 11 : 409 – 412 .
   Google Scholar
• Liniger , W. and Willoughby , R. A. 1970 . Efficient integration method for stiff systems of ordinary differential equations . SIAM J. Numer. Anal. , 7 : 47 – 66 .
   Web of Science ®Google Scholar
• Neta , B. 1979 . A sixth-order family of methods for nonlinear equations . Int. J. Comput. Math. , 7 : 157 – 161 .
   Web of Science ®Google Scholar
• Neta , B. 1981 . On a family of multipoint methods for nonlinear equations . Int. J. Comput. Math. , 9 : 353 – 361 .
   Web of Science ®Google Scholar
• Noor , M. A. and Ahmad , F. 2006 . Numerical comparison of iterative methods for solving nonlinear equations . Appl. Math. Comput. , 180 : 167 – 172 .
   Web of Science ®Google Scholar
• Noor , M. A. , Ahmad , F. and Javeed , S. 2006 . Two-step iterative methods for nonlinear equations . Appl. Math. Comput. , 181 : 1068 – 1075 .
   Web of Science ®Google Scholar
• Ortega , J. M. and Rheinboldt , W. G. 1970 . Iterative Solution of Nonlinear Equations in Several Variables , New York : Academic Press .
   Google Scholar
• Ostrowski , A. M. 1973 . Solution of Equations in Euclidean and Banach Space , 3 , New York and London : Academic Press .
   Google Scholar
• Traub , J. F. 1964 . Iterative Methods for the Solution of Equations , Englewood Cliffs, NJ : Prentice Hall .
   Google Scholar
• Wang , K. and Feng , X. L. 2010 . New predictor–corrector methods for solving nonlinear equations . J. Appl. Math. Comput. , 34 ( 1–2 ) : 299 – 315 .
   Google Scholar
• Werner , W. 1981 . Some efficient algorithms for the solution of a single nonlinear equation . Int. J. Comput. Math. , 9 : 141 – 149 .
   Web of Science ®Google Scholar
• Wu , X. Y. 1997 . Exact exponentially fitted method for solving stiff ordinary differential equations (in Chinese) . J. Nanjing Univ. Natural Sci. , 33 : 1 – 6 .
   Google Scholar
• Wu , X. Y. 1999 . A significant improvement on Newton's iterative method . Appl. Math. Mech. , 20 : 367 – 370 .
   Google Scholar
• Wu , X. Y. , Shen , Z. H. and Xia , J. L. 2003 . An improved regula falsi method with quadratic convergence of both diameter and point for enclosing simple zeros of nonlinear equations . Appl. Math. Comput. , 144 : 381 – 388 .
   Web of Science ®Google Scholar