Janak Raj Sharma
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View article: Convergence analysis of iterative compositions in nonlinear modeling: exploring semilocal and local convergence phenomena
Convergence analysis of iterative compositions in nonlinear modeling: exploring semilocal and local convergence phenomena Open
In this work, a comprehensive analysis of a multi-step iterative composition for nonlinear equation is performed, providing insights into both local and semilocal convergence properties. The analysis covers a wide range of applications, el…
View article: Development and analysis of an efficient Jacobian-free method for systems of nonlinear equations
Development and analysis of an efficient Jacobian-free method for systems of nonlinear equations Open
A multi-step derivative-free iterative technique is developed by extending the well-known Traub-Steffensen iteration for solving the systems of nonlinear equations. Keeping in mind the computational aspects, the general idea to construct t…
View article: A Harmonic-Type Method for Nonlinear Equations in Banach Space
A Harmonic-Type Method for Nonlinear Equations in Banach Space Open
In this work, we investigate the local and semi-local convergence of a harmonic mean Newton-type fourth-order technique for estimating the locally unique solutions of nonlinear systems in Banach spaces. The local analysis is established in…
View article: An Optimal Family of Eighth-Order Methods for Multiple-Roots and Their Complex Dynamics
An Optimal Family of Eighth-Order Methods for Multiple-Roots and Their Complex Dynamics Open
We present a new family of optimal eighth-order numerical methods for finding the multiple zeros of nonlinear functions. The methodology used for constructing the iterative scheme is based on the approach called the ‘weight factor approach…
View article: Optimal Fourth-Order Methods for Multiple Zeros: Design, Convergence Analysis and Applications
Optimal Fourth-Order Methods for Multiple Zeros: Design, Convergence Analysis and Applications Open
Nonlinear equations are frequently encountered in many areas of applied science and engineering, and they require efficient numerical methods to solve. To ensure quick and precise root approximation, this study presents derivative-free ite…
View article: Seventh Order Derivative-Free Methods for Non-differentiable Operator Equations
Seventh Order Derivative-Free Methods for Non-differentiable Operator Equations Open
In nonlinear problems where function’s derivatives are difficult or expensive to compute, derivative-free iterative methods are good options to find the numerical solution. One of the important parts in the development of such methods is t…
View article: Three-Step Derivative-Free Method of Order Six
Three-Step Derivative-Free Method of Order Six Open
Derivative-free iterative methods are useful to approximate the numerical solutions when the given function lacks explicit derivative information or when the derivatives are too expensive to compute. Exploring the convergence properties of…
View article: Numerical Solution of Nonlinear Problems with Multiple Roots Using Derivative-Free Algorithms
Numerical Solution of Nonlinear Problems with Multiple Roots Using Derivative-Free Algorithms Open
In the study of systems’ dynamics the presence of symmetry dramatically reduces the complexity, while in chemistry, symmetry plays a central role in the analysis of the structure, bonding, and spectroscopy of molecules. In a more general c…
View article: SIMPLE AND EFFICIENT FIFTH ORDER SOLVERS FOR SYSTEMS OF NONLINEAR PROBLEMS
SIMPLE AND EFFICIENT FIFTH ORDER SOLVERS FOR SYSTEMS OF NONLINEAR PROBLEMS Open
In this study, two multi-step iterative techniques of fifth order convergence are explored to solve nonlinear equations. The techniques are designed with the prime objective of keeping the computational cost as low as possible. To claim th…
View article: Extended comparison between two Newton–Jarratt sixth order schemes for nonlinear models under the same set of conditions
Extended comparison between two Newton–Jarratt sixth order schemes for nonlinear models under the same set of conditions Open
Two sixth order convergence order schemes are compared and extended to solve Banach space valued models. Earlier studies have used derivatives and Taylor expansions up to order seven to show the convergence order in a finite-dimensional Eu…
View article: A Unified Local-Semilocal Convergence Analysis of Efficient Higher Order Iterative Methods in Banach Spaces
A Unified Local-Semilocal Convergence Analysis of Efficient Higher Order Iterative Methods in Banach Spaces Open
To deal with the estimation of the locally unique solutions of nonlinear systems in Banach spaces, the local as well as semilocal convergence analysis is established for two higher order iterative methods. The given methods do not involve …
View article: On the Local Convergence of a (p + 1)-Step Method of Order 2p + 1 for Solving Equations
On the Local Convergence of a (p + 1)-Step Method of Order 2p + 1 for Solving Equations Open
The local convergence of a generalized (p+1)-step iterative method of order 2p+1 is established in order to estimate the locally unique solutions of nonlinear equations in the Banach spaces. In earlier studies, convergence analysis for the…
View article: Design and analysis of a faster King-Werner-type derivative free method
Design and analysis of a faster King-Werner-type derivative free method Open
We introduce a new faster King-Werner-type derivative-free method for solving nonlinear equations. The local as well as semi-local convergence analysis is presented under weak center Lipschitz and Lipschitz conditions. The convergence orde…
View article: Convergence Analysis and Dynamical Nature of an Efficient Iterative Method in Banach Spaces
Convergence Analysis and Dynamical Nature of an Efficient Iterative Method in Banach Spaces Open
We study the local convergence analysis of a fifth order method and its multi-step version in Banach spaces. The hypotheses used are based on the first Fréchet-derivative only. The new approach provides a computable radius of convergence, …
View article: A Family of Derivative Free Optimal Fourth Order Methods for Computing Multiple Roots
A Family of Derivative Free Optimal Fourth Order Methods for Computing Multiple Roots Open
Many optimal order multiple root techniques, which use derivatives in the algorithm, have been proposed in literature. But contrarily, derivative free optimal order techniques for multiple root are almost nonexistent. By this as an inspira…
View article: Generating Optimal Eighth Order Methods for Computing Multiple Roots
Generating Optimal Eighth Order Methods for Computing Multiple Roots Open
There are a few optimal eighth order methods in literature for computing multiple zeros of a nonlinear function. Therefore, in this work our main focus is on developing a new family of optimal eighth order iterative methods for multiple ze…
View article: A Novel Family of Efficient Weighted-Newton Multiple Root Iterations
A Novel Family of Efficient Weighted-Newton Multiple Root Iterations Open
We propose a novel family of seventh-order iterative methods for computing multiple zeros of a nonlinear function. The algorithm consists of three steps, of which the first two are the steps of recently developed Liu–Zhou fourth-order meth…
View article: On Derivative Free Multiple-Root Finders with Optimal Fourth Order Convergence
On Derivative Free Multiple-Root Finders with Optimal Fourth Order Convergence Open
A number of optimal order multiple root techniques that require derivative evaluations in the formulas have been proposed in literature. However, derivative-free optimal techniques for multiple roots are seldom obtained. By considering thi…
View article: An Optimal Fourth Order Derivative-Free Numerical Algorithm for Multiple Roots
An Optimal Fourth Order Derivative-Free Numerical Algorithm for Multiple Roots Open
A plethora of higher order iterative methods, involving derivatives in algorithms, are available in the literature for finding multiple roots. Contrary to this fact, the higher order methods without derivatives in the iteration are difficu…
View article: Optimal One-Point Iterative Function Free from Derivatives for Multiple Roots
Optimal One-Point Iterative Function Free from Derivatives for Multiple Roots Open
We suggest a derivative-free optimal method of second order which is a new version of a modification of Newton’s method for achieving the multiple zeros of nonlinear single variable functions. Iterative methods without derivatives for mult…
View article: Local Convergence of an Efficient Multipoint Iterative Method in Banach Space
Local Convergence of an Efficient Multipoint Iterative Method in Banach Space Open
We discuss the local convergence of a derivative-free eighth order method in a Banach space setting. The present study provides the radius of convergence and bounds on errors under the hypothesis based on the first Fréchet-derivative only.…
View article: Local Convergence and Attraction Basins of Higher Order, Jarratt-Like Iterations
Local Convergence and Attraction Basins of Higher Order, Jarratt-Like Iterations Open
We studied the local convergence of a family of sixth order Jarratt-like methods in Banach space setting. The procedure so applied provides the radius of convergence and bounds on errors under the conditions based on the first Fréchet-deri…
View article: On a Class of Optimal Fourth Order Multiple Root Solvers without Using Derivatives
On a Class of Optimal Fourth Order Multiple Root Solvers without Using Derivatives Open
Many optimal order multiple root techniques involving derivatives have been proposed in literature. On the contrary, optimal order multiple root techniques without derivatives are almost nonexistent. With this as a motivational factor, her…
View article: Convergence Analysis and Complex Geometry of an Efficient Derivative-Free Iterative Method
Convergence Analysis and Complex Geometry of an Efficient Derivative-Free Iterative Method Open
To locate a locally-unique solution of a nonlinear equation, the local convergence analysis of a derivative-free fifth order method is studied in Banach space. This approach provides radius of convergence and error bounds under the hypothe…
View article: An Efficient Class of Weighted-Newton Multiple Root Solvers with Seventh Order Convergence
An Efficient Class of Weighted-Newton Multiple Root Solvers with Seventh Order Convergence Open
In this work, we construct a family of seventh order iterative methods for finding multiple roots of a nonlinear function. The scheme consists of three steps, of which the first is Newton’s step and last two are the weighted-Newton steps. …
View article: One-Point Optimal Family of Multiple Root Solvers of Second-Order
One-Point Optimal Family of Multiple Root Solvers of Second-Order Open
This manuscript contains the development of a one-point family of iterative functions. The family has optimal convergence of a second-order according to the Kung-Traub conjecture. This family is used to approximate the multiple zeros of no…
View article: On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems
On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems Open
We propose a derivative-free iterative method with fifth order of convergence for solving systems of nonlinear equations. The scheme is composed of three steps, of which the first two steps are that of third order Traub-Steffensen-type met…
View article: An Efficient Derivative Free One-Point Method with Memory for Solving Nonlinear Equations
An Efficient Derivative Free One-Point Method with Memory for Solving Nonlinear Equations Open
We propose a derivative free one-point method with memory of order 1.84 for solving nonlinear equations. The formula requires only one function evaluation and, therefore, the efficiency index is also 1.84. The methodology is carried out by…
View article: Development of Optimal Eighth Order Derivative-Free Methods for Multiple Roots of Nonlinear Equations
Development of Optimal Eighth Order Derivative-Free Methods for Multiple Roots of Nonlinear Equations Open
A number of higher order iterative methods with derivative evaluations are developed in literature for computing multiple zeros. However, higher order methods without derivative for multiple zeros are difficult to obtain and hence such met…
View article: On a Bi-Parametric Family of Fourth Order Composite Newton–Jarratt Methods for Nonlinear Systems
On a Bi-Parametric Family of Fourth Order Composite Newton–Jarratt Methods for Nonlinear Systems Open
We present a new two-parameter family of fourth-order iterative methods for solving systems of nonlinear equations. The scheme is composed of two Newton–Jarratt steps and requires the evaluation of one function and two first derivatives in…