Iterative methods for solving scalar equations

Aslam

Discrete Dynamics in Nature and Society

et al. 2018

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We introduce a new family of iterative methods for solving mathematical models whose governing equations are nonlinear in nature. The new family gives several iterative schemes as special cases. We also give the convergence analysis of our proposed methods. In order to demonstrate the improved performance of newly developed methods, we consider some nonlinear equations along with two complex mathematical models. The graphical analysis for these models is also presented.

Section: Introductionmentioning

confidence: 99%

New Family of Iterative Methods for Solving Nonlinear Models

Aslam

Discrete Dynamics in Nature and Society

et al. 2018

Self Cite

Some New Iterative Techniques for the Problems Involving Nonlinear Equations

Int. J. Comput. Methods

Aslam

Rafiq

2019

We develop some new iterative methods, using decomposition technique, for solving the problems which involve nonlinear equations. Importantly, these methods include the generalization of some well-known existing methods. We prove the convergence criteria of our newly proposed methods. Various test examples are considered to validate the efficiency of our new methods. We also give the numerical as well as graphical analysis for two mathematical models to endorse the performance of these methods.

Some Recent Modifications of Fixed Point Iterative Schemes for Computing Zeros of Nonlinear Equations

et al. 2022

In computational mathematics, it is a matter of deep concern to recognize which of the given iteration schemes converges quickly with lesser error to the desired solution. Fixed point iterative schemes are constructed to be used for solving equations emerging in many fields of science and engineering. These schemes reformulate a nonlinear equation f s = 0 into a fixed point equation of the form s = g s ; such application determines the solution of the original equation via the support of fixed point iterative method and is subject to existence and uniqueness. In this manuscript, we introduce a new modified family of fixed point iterative schemes for solving nonlinear equations which generalize further recursive methods as particular cases. We also prove the convergence of our suggested schemes. We also consider some of the mathematical models which are categorically nonlinear in essence to authenticate the performance and effectiveness of these schemes which can be seen as an expansion and rationalization of some existing techniques.