On Iterative Methods for Solving Nonlinear Equations in Quantum Calculus

Sana, Gul; Mohammed, Pshtiwan Othman; Shin, Dong Yun; Noor, Muhammad Aslam; Oudat, Mohammad Salem

doi:10.3390/fractalfract5030060

Cited by 14 publications

(12 citation statements)

References 33 publications

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“…Let r be the simple zero of f is satisfactorily differentiable. Between n  and 1 n  + has developed a bond of r for the convergence rate of HNIT (1). Suppose ( ) ( ) ( ) ( )…”

Section: Proofmentioning

confidence: 99%

“…Efforts were made with an efficient approximate solution of the various NLP types of ( ) 0 fx= for exploring the modified and hybrid NIT scheme, i.e., HNIT (1). The HNIT model was developed as the family of bracketing iterative techniques (BITs) with NRIT and TSE crossbreed contemplations and found an excellent work performance.…”

Section: Hybrid Numerical Iterative Techniquementioning

confidence: 99%

“…Such solutions to real-world challenges and problems can be logically approximated with applied mathematics including algebra, geometry, engineering, physical, social, biological, natural sciences and so on. Various studies have discovered the different ways of order iterative methods to solve nonlinear problems [1]. Initially, Traub [2] presented the study of iterative strategies for solving nonlinear equations and proposed a fundamental quadratic convergent Newton iterative method for solving nonlinear equations, often frequently taking advantage of the literature.…”

Section: Introductionmentioning

confidence: 99%

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Convergence rate for the hybrid iterative technique to explore the real root of nonlinear problems

Shaikh

Memon

et al. 2023

Mehran Univ. res. j. eng. technol.

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This study explored the convergence rate of the hybrid numerical iterative technique (HNIT) for the solution of nonlinear problems (NLPs) of one variable ( f (x) = 0) . It is sightseen that convergence rate is two for the HNIT. By the HNIT, several algebraic and transcendental NLPs of one variable have been illustrated as an approximate real root for efficient performance. In many instances, HNIT is more vigorous and attractive than well-known conventional iterative techniques (CITs). The computational tool MATLAB has been used for the solution of iterative techniques.

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“…Let r be the simple zero of f is satisfactorily differentiable. Between n  and 1 n  + has developed a bond of r for the convergence rate of HNIT (1). Suppose ( ) ( ) ( ) ( )…”

Section: Proofmentioning

confidence: 99%

Section: Hybrid Numerical Iterative Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Convergence rate for the hybrid iterative technique to explore the real root of nonlinear problems

Shaikh

Memon

et al. 2023

Mehran Univ. res. j. eng. technol.

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“…The main advantage of fractional order differential equations is that they produce accurate and stable results. Therefore, these equations represent a significant class of differential equations [11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

An efficient approach to solving fractional Van der Pol–Duffing jerk oscillator

El‐Dib¹

2022

Commun. Theor. Phys.

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The motive behind the current work is to perform the solution of the Van der Pol–Duffing jerk oscillator, involving fractional-order by the simplest method. An effective procedure has been introduced for executing the fractional-order by utilizing a new method without the perturbative approach. The approach depends on converting the fractional nonlinear oscillator to a linear oscillator with an integer order. The sincerity of the established results is justified by providing a suitable example of nonlinear oscillators. The obtained analytical solutions are supported by the numerical simulation results. The method applied here does not require hard mathematical work, which makes it distinct from other methods. The simplicity of the present approach provides extra advantages for fractional-order solutions. This method enriches the analysis with more details in new dimensions.

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“…This strategy combines the Sumudu transform method with an iterative method, two potent approaches. An iterative method (IM) has been presented by Daftardar-Gejji and Jafari to solve linear and nonlinear functional equations [37][38][39][40]. The IM has been effectively applied in many kinds of investigation to solve some linear and nonlinear PDEs and ODEs, NDDEs, higher-order integro-DEs, two-dimensional nonlinear Sine Gordon equation (NLSGE), and Korteweg-de Vries equations [25,[41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method

Moltot

Deresse

2022

Advances in Mathematical Physics

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In this study, an efficient analytical method called the Sumudu Iterative Method (SIM) is introduced to obtain the solutions for the nonlinear delay differential equation (NDDE). This technique is a mixture of the Sumudu transform method and the new iterative method. The Sumudu transform method is used in this approach to solve the equation’s linear portion, and the new iterative method’s successive iterative producers are used to solve the equation’s nonlinear portion. Some basic properties and theorems which help us to solve the governing problem using the suggested approach are revised. The benefit of this approach is that it solves the equations directly and reliably, without the prerequisite for perturbations or linearization or extensive computer labor. Five sample instances from the DDEs are given to confirm the method’s reliability and effectiveness, and the outcomes are compared with the exact solution with the assistance of tables and graphs after taking the sum of the first eight iterations of the approximate solution. Furthermore, the findings indicate that the recommended strategy is encouraging for solving other types of nonlinear delay differential equations.

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On Iterative Methods for Solving Nonlinear Equations in Quantum Calculus

Cited by 14 publications

References 33 publications

Convergence rate for the hybrid iterative technique to explore the real root of nonlinear problems

Convergence rate for the hybrid iterative technique to explore the real root of nonlinear problems

An efficient approach to solving fractional Van der Pol–Duffing jerk oscillator

Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method

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