کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4631067 | 1340616 | 2011 | 8 صفحه PDF | دانلود رایگان |
In this paper, a family of fourth-order Steffensen-type two-step methods is constructed to make progress in including Ren–Wu–Bi’s methods [H. Ren, Q. Wu, W. Bi, A class of two-step Steffensen type methods with fourth-order convergence, Appl. Math. Comput. 209 (2009) 206–210] and Liu–Zheng–Zhao’s method [Z. Liu, Q. Zheng, P. Zhao, A variant of Steffensens method of fourth-order convergence and its applications, Appl. Math. Comput. 216 (2010) 1978–1983] as its special cases. Its error equation and asymptotic convergence constant are deduced. The family provides the opportunity to obtain derivative-free iterative methods varying in different rates and ranges of convergence. In the numerical examples, the family is not only compared with the related methods for solving nonlinear equations, but also applied in the solution of BVPs of nonlinear ODEs by the finite difference method and the multiple shooting method.
Journal: Applied Mathematics and Computation - Volume 217, Issue 21, 1 July 2011, Pages 8196–8203