A variant of Steffensen’s method of fourth-order convergence and its applications |
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| Authors: | Zhongli Liu Quan Zheng |
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| Institution: | a College of Biochemical Engineering, Beijing Union University, Beijing 100023, China
b College of Sciences, North China University of Technology, Beijing 100144, China |
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| Abstract: | In this paper, a variant of Steffensen’s method of fourth-order convergence for solving nonlinear equations is suggested. Its error equation and asymptotic convergence constant are proven theoretically and demonstrated numerically. The derivative-free method only uses three evaluations of the function per iteration to achieve fourth-order convergence. Its applications on systems of nonlinear equations and boundary-value problems of nonlinear ODEs are showed as well in the numerical examples. |
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| Keywords: | Nonlinear equations Newton&rsquo s method Steffensen&rsquo s method Derivative free Fourth-order convergence ODEs |
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