Applied Science and Computer Mathematics

Newton-type methods for solving nonlinear equations using contra harmonic mean

  • By Yanlin Tao
  • Applied Science and Computer Mathematics, 1(1) (2020): 32-39

Abstract

Newton’s method has been modified in recent years to find a simple root of non-linear equation with accelerated convergence. In this paper, two Newton-like methods for solving a nonlinear equation are proposed. These methods use contra harmonic mean instead of arithmetic mean while using the trapezoidal and Simpson’s integration rules in the Newton’s theorem. The order of convergence of the new methods is three and increases to five for one of the methods satisfying an additional condition. Numerical examples and their results are provided to compare the efficiency of the new methods with few other similar methods.