Abstract
In the study of dynamics of physical systems an important role is played by symmetry principles. As an example in classical physics, symmetry plays a role in quantum physics, turbulence and similar theoretical models. We end up having to deal with an equation whose solution we desire to be in a closed form. But obtaining a solution in such form is achieved only in special cases. Hence, we resort to iterative schemes. There is where the novelty of our study lies, as well as our motivation for writing it. We have a very limited literature with eighth-order convergent iteration functions that can handle multiple zeros m≥1. Therefore, we suggest an eighth-order scheme for multiple zeros having optimal convergence along with fast convergence and uncomplicated structure. We develop an extensive convergence study in the main theorem that illustrates eighth-order convergence of our scheme. Finally, the applicability and comparison was illustrated on real life problems, e.g., Van der Waal’s equation of state, Chemical reactor with fractional conversion, continuous stirred reactor and multi-factor problems, etc., with existing schemes. These examples further show the superiority of our schemes over the earlier ones.
Highlights
One of the problems of great significance and difficulty in the subject of computational mathematics is finding the multiple zeros for f ( x ) ( f : D ⊂ R → R a sufficiently differentiable function in D)
We develop an eighth-order scheme for multiple zeros with simple and compact body design
We demonstrate the same with an optimal eighth-order iteration function developed by Behl et al [26], which is given by f
Summary
One of the problems of great significance and difficulty in the subject of computational mathematics is finding the multiple zeros for f ( x ) ( f : D ⊂ R → R a sufficiently differentiable function in D). That is why in practice, we obtain an approximated and efficient solution up to any specific degree of accuracy by the means of an iterative procedure This is one of the main reasons that researchers have been making great efforts to develop iteration functions over the past few decades. We know that there is always a scope in the research to obtain better approximation techniques with simple and compact body structure While keeping all these things in our mind, we present an eighth-order iteration scheme having optimal convergence for obtaining the multiple solutions of scalar equation which is better than the existing ones.
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