Aug 2026· Iraqi Journal of Science· pp. 4479-4490· 0 citations· 31 references
Abstract
In this paper, we propose and analyze a new one-parameter family of two-step iterative methods without requiring higher derivatives for solving nonlinear equations. This family is constructed based on a Newton-type method utilizing the Heron mean, a predictor-corrector technique, and an appropriate choice of derivative approximations. Each iteration of the new methods requires two function evaluations and one first derivative evaluation. Convergence analysis shows that the proposed methods achieve third- and fourth-order convergence, with corresponding efficiency indices of 1.44225 and 1.58740, respectively. Numerical examples are provided to demonstrate the performance and efficiency of the proposed methods.
In this paper, a new double-step (NDS) iteration method is proposed for solving a broad class of complex continuous Sylvester equations. Some sufficient conditions guaranteeing the convergence of the NDS iteration method are studied and the quasi-optimal parameter is given. Moreover, to reduce the computational cost, a...
Xu Li, Ning He, Jian-Sheng Feng· Journal of Mathematical Stud...· 0 citations
In this paper, two - step hybrid numerical methods for direct solution of initial value problems of second order ordinary differential equations are proposed in this study. Chebyshev polynomials of the first kind are used as basic function for the approximate solution. The collocation and interpolation equations are ge...
A. Bala, Nosakhare Fidelis Uwadia, Odiachi Ifeanyi Sunday et al.· Nigerian Journal of Physics· 0 citations
This paper introduces a novel variable-step block hybrid method for the direct solution of general third-order initial value problems. The proposed approach combines quasilinearization with an embedded procedure to enhance accuracy and computational efficiency. Rigorous analysis establishes the convergence and $A$-stab...
S. D. Yakubu, P. Sibanda, S. Goqo et al.· Armenian Journal of Mathemat...· 0 citations
In this paper, a new way to improve approximation operators is proposed. Two well-known methods are combined: the linear combination of the classic Bernstein operator and the iteration technique. The main goal is to make the convergence to the function faster and to obtain more accurate numerical results for practical...
A. Jaddoa, Hanadi Abdulsattar, N. Jassim· Journal of Numerical Analysi...· 0 citations
In this article, we present a new two-step cubic spline method of O(2,4) for estimating the numerical solution of a 1D nonlinear parabolic partial differential equation with appropriate conditions at the initial time level and Dirichlet conditions along the boundary. Furthermore, we present a new single-segment, group-...
J. Talwar, R. Mohanty· Acta Universitatis Sapientia...· 0 citations
This study considers an application of differential transform method (DTM) to solving linear
and nonlinear eleventh order two-point boundary value problems discussed in [S.S. Siddiqi, G. Akram and I.
Zulfiqar. Solution of eleventh order boundary value problems using variational iteration technique. European
Journal...
Amjad Hussain, S. Mohyud-Din, A. Yıldırım· Journal of Information and C...· 0 citations
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