On iterative techniques for estimating all roots of nonlinear equation and its system with application in differential equation

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Shams M., Rafiq N., Kausar N., Agarwal P., Park C., Mir N. A.

ADVANCES IN DIFFERENCE EQUATIONS, vol.2021, no.1, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2021 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1186/s13662-021-03636-x
  • Keywords: Single and all roots, Nonlinear system of equations, Iterative methods, Simultaneous methods, Basins of attraction, Boundary value problems, SIMULTANEOUS APPROXIMATION, NEWTON METHOD, CONVERGENCE, ORDER, ZEROS


In this article, we construct a family of iterative methods for finding a single root of nonlinear equation and then generalize this family of iterative methods for determining all roots of nonlinear equations simultaneously. Further we extend this family of root estimating methods for solving a system of nonlinear equations. Convergence analysis shows that the order of convergence is 3 in case of the single root finding method as well as for the system of nonlinear equations and is 5 for simultaneous determination of all distinct and multiple roots of a nonlinear equation. The computational cost, basin of attraction, efficiency, log of residual and numerical test examples show that the newly constructed methods are more efficient as compared to the existing methods in literature.