A Family of Optimal Eighth Order Multiple Root Finders with Multivariate Weight Function

Abstract

Finding repeated zero for a nonlinear equation \(f(x)=0\), \(f:I\subseteq R\rightarrow R\), has always been of much interest and attention due to it’s wide applications in many fields of science and engineering. The modified Newton’s method is usually applied to solve this problem. Keeping in view that very few optimal higher order convergent methods exist for multiple roots, we present a new family of optimal eighth order convergent iterative methods for multiple roots with known multiplicity involving multivariate weight function. The numerical performance of the proposed methods is analyzed extensively along with the basins of attractions. Real life models from Life Science, Engineering and Physics are considered for the sake of comparison. The numerical experiments show that our proposed methods are efficient for determining multiple roots of non-linear equations.