Stability analysis of fourth-order iterative method for finding multiple roots of non-linear equations

[1]R. Behl, Alicia Cordero, S .S. Motsa, J. R. Torregrosa. (2015) On developing fourth-order optimal families of methods for multiple roots and their dynamics, Appl. Math. Comput., 265, 520–532. Behl R. Alicia Cordero Motsa S .S. Torregrosa J. R. 2015 On developing fourth-order optimal families of methods for multiple roots and their dynamics Appl. Math. Comput 265 520–532Search in Google Scholar

[2]R. Behl, A. Cordero, S. S. Motsa, J. R. Torregrosa and V. Kanwar. (2016), An optimal fourth-order family of methods for multiple roots and its dynamics, Numer. Algor., 71, 775–796. Behl R. Cordero A. Motsa S. S. Torregrosa J. R. Kanwar V. 2016 An optimal fourth-order family of methods for multiple roots and its dynamics Numer. Algor 71 775–796Search in Google Scholar

[3]P. Blanchard. (1984), Complex analytic dynamics on the Riemann sphere, Bull. Amer. Math. Soc., 11(1), 85–141. Blanchard P. 1984 Complex analytic dynamics on the Riemann sphere Bull. Amer. Math. Soc 111 85141Search in Google Scholar

[4]J. L. Hueso, E. Martinez and C. Teruel. (2015), Determination of multiple roots of nonlinear equations and applications, J. Math. Chem., 53, 880–892. Hueso J. L. Martinez E. Teruel C. 2015 Determination of multiple roots of nonlinear equations and applications J. Math. Chem 53 880–892Search in Google Scholar

[5]H. T. Kung and J. F. Traub. (1974), Optimal order of one-point and multipoint iteration, J. ACM, 21, 643–651. Kung H. T. Traub J. F. 1974 Optimal order of one-point and multipoint iteration J. ACM 21 643651Search in Google Scholar

[6]E. Schröder. (1870), unendlich viele Algorithmen zur Auflösung der Gleichungen, Math. Ann., 2, 317–365. Schröder E. 1870 unendlich viele Algorithmen zur Auflösung der Gleichungen Math. Ann 2 317–365Search in Google Scholar

[7]J. R. Sharma and R. Sharma. (2010), Modified Jarratt method for computing multiple roots, Appl. Math. Comput., 217, 878–881. Sharma J. R. Sharma R. 2010 Modified Jarratt method for computing multiple roots Appl. Math. Comput 217 878–881Search in Google Scholar

[8]J. R. Sharma and R. Sharma. (2011), New third and fourth order nonlinear solvers for computing multiple roots, Appl. Math. Comput., 217, 9756–9764. Sharma J. R. Sharma R. 2011 New third and fourth order nonlinear solvers for computing multiple roots Appl. Math. Comput 217 9756–9764Search in Google Scholar

[9]L. Shengguo, L. Xiangke and C. Lizhi. (2009), A new fourth-order iterative method for finding multiple roots of nonlinear equations, Appl. Math. Comput., 215, 1288–1292. Shengguo L. Xiangke L. Lizhi C. 2009 A new fourth-order iterative method for finding multiple roots of nonlinear equations Appl. Math. Comput 215 1288–1292Search in Google Scholar

[10]A. Singh and J. P. Jaiswal. (2015), An efficient family of optimal fourth-order iterative methods for finding multiple roots of nonlinear equations, Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci., 85, 439–450. Singh A. Jaiswal J. P. 2015 An efficient family of optimal fourth-order iterative methods for finding multiple roots of nonlinear equations Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci 85 439–450Search in Google Scholar

[11]F. Soleymani, D. K. R. Babajee and T. Lotfi. (2013), On a numerical technique for finding multiple zeros and its dynamic, J. Egyptian Math. Soc., 21, 346–353. Soleymani F. Babajee D. K. R. Lotfi T. 2013 On a numerical technique for finding multiple zeros and its dynamic J. Egyptian Math. Soc 21 346–353Search in Google Scholar

[12]F. Soleymani and D. K. R. Babajee. (2013), Computing multiple zeros using a class of quartically convergent methods, Alexandria Engg. J., 52, 531–541. Soleymani F. Babajee D. K. R. 2013 Computing multiple zeros using a class of quartically convergent methods Alexandria Engg. J 52 531–541Search in Google Scholar