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Variant of Newton’s Method Using Simpson’s 3/8th Rule

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Abstract

The main objective of this work is to present a new closed type third order variant of Newton’s method for solving system of nonlinear equations, which not only accelerates the Newton’s method but also removes its certain limitations. For this purpose we applied Simpson’s three eighth rule instead of trapezoid and rectangle in approximating the integral and thereby reducing the error. Numerical results show that the method is superior to the same order existing methods and well compete with some higher order methods.

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Acknowledgements

Authors are thankful to reviewers for their valuable suggestions to improve the manuscript.

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Correspondence to Arvind K. Singh.

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Singh, M.K., Singh, A.K. Variant of Newton’s Method Using Simpson’s 3/8th Rule. Int. J. Appl. Comput. Math 6, 20 (2020). https://doi.org/10.1007/s40819-020-0770-4

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Keywords

  • Newton’s method
  • Weak condition
  • Simpson’s 3/8th formula
  • Order of convergence

Mathematics Subject Classification

  • 65H04
  • 65H05