New iterative technique for solving a system of nonlinear equations

In the recent literature, very few high-order Jacobian-free methods with memory for solving nonlinear systems appear. In this paper, we introduce a new variant of King’s family with order four to solve nonlinear systems along with its convergence analysis. The proposed family requires two divided difference operators and to compute only one inverse of a matrix per iteration. Furthermore, we have extended the proposed scheme up to the sixth-order of convergence with two additional functional evaluations. In addition, these schemes are further extended to methods with memory. We illustrate their applicability by performing numerical experiments on a wide variety of practical problems, even big-sized. It is observed that these methods produce approximations of greater accuracy and are more efficient in practice, compared with the existing methods.

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“…Example 1. Let us firstly consider the problem of kinematic synthesis for steering, that was described in [21][22][23][24].…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…x (j+1) − x (j) ACOC SM 4 Example 2. Now, we focus our studies in the Van der Pol equation [22,25], defined as:…”

Section: Cases J ψ(X (J) )mentioning

confidence: 99%

Memory in a New Variant of King’s Family for Solving Nonlinear Systems

et al. 2020

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“…Authors In 58 have suggested a iterative methods for solving nonlinear equations involving only first derivative of the function. A family of iterative methods for solving the system of nonlinear equations has been presented 59 . Authors in 60 have suggested and analyzed some unique recurrence relations which generate different classes of iterative techniques for investigating nonlinear problems using the coupled system of equations.…”

Section: Introductionmentioning

confidence: 99%

Comparative study of generalized couette flow of couple stress fluid using optimal homotopy asymptotic method and new iterative method

Farooq

Khan

Nawaz

et al. 2021

Sci Rep

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In this research work, we have studied the steady generalized Couette flow of couple stress fluid between two parallel plates considering the non-isothermal effects. The governing equations that are, continuity, momentum and energy equations are reduced to ordinary differential equations. The Optimal Homotopy Asymptotic Method (OHAM) and New Iterative Method (NIM) are used to solve this coupled system of differential equations. Using the said methods, we have obtained expressions for velocity profile, temperature distribution, volume flux, average velocity and shear stress. The results of OHAM and NIM are compared numerically as well as graphically and a tremendous agreement is attained.

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“…[27][28][29] Very recently, the IM was employed for solving various kinds of nonlinear mathematical problems that can be found in the following literatures. [30][31][32][33] In this research, we have applied the IM to unravel the nonlinear chemical kinetics equations. The main advantages of IM are its easy solutions procedure, and sometimes, within a few iterations, we can obtain the decent accuracy.…”

Section: Introductionmentioning

confidence: 99%

A novel iterative method for solving chemical kinetics system

Chowdhury

Ghosh

Aznam

et al. 2021

Journal of Low Frequency Noise, Vibration and Active Control

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The purpose of this research is to impose a semi-analytical method called the iterative method to the chemical kinetics system, which appears in the form of a system of ordinary differential equations. To test the accuracy of the standard iterative method, we have applied the classical fourth-order Runge–Kutta method and the iterative method to the chemical kinetics system. It is significantly notable that approximate analytical precisions of standard iterative method made a high agreement with those obtained from the fourth-order Runge–Kutta technique. Numerical outputs and solution procedures indicate that iterative method can be easily applicable to a large class of scientific numeric applications with high accuracy.

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New iterative technique for solving a system of nonlinear equations

Cited by 12 publications

References 43 publications

Memory in a New Variant of King’s Family for Solving Nonlinear Systems

Memory in a New Variant of King’s Family for Solving Nonlinear Systems

Comparative study of generalized couette flow of couple stress fluid using optimal homotopy asymptotic method and new iterative method

A novel iterative method for solving chemical kinetics system

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