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Article
Mathematics, Interdisciplinary Applications
Guanqun LI et al.
Summary: Large-scale hydraulic fracturing is crucial for efficient shale oil production, but the mechanisms of fracturing fluid flow in shale micropores and the impact of shale microstructure and physical properties are not well understood. This lack of understanding hinders the optimization of fracturing flowback and limits shale oil recovery enhancement. This study analyzes the characteristics of shale pores using SEM and XRD experiments, finding multiple pore types including organic pores, brittle mineral pores, and clay pores. The study investigates the influence of cross-section shapes on capillary force and analyzes the dynamics of imbibition in different pore types. A shale semi-analytical solution that considers imbibition time, fluid properties, pore cross-section shapes, tortuosity, and forced pressure is established using a shale multi-pores physical model and fractal theory.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Interdisciplinary Applications
Mudassir Shams et al.
Summary: In this study, a new family of inverse iterative numerical techniques is developed to extract all roots of a nonlinear equation simultaneously. Convergence analysis shows that the proposed methods have local 10th-order convergence. Compared to other methods, the inverse simultaneous iterative techniques provide initial estimations to exact roots within a given tolerance while using fewer function evaluations in each iterative step.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Applied
Alicia Cordero et al.
Summary: This paper proposes a procedure to transform any iterative scheme into a method for approximating all roots of nonlinear equations simultaneously. The proposed scheme achieves a convergence order twice that of the original method. Numerical tests validate the theoretical results and compare the proposed schemes with other existing methods for simultaneous roots of polynomial and non-polynomial functions.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Krzysztof Gdawiec et al.
Summary: This paper visually investigates the dynamics and stability of replacing classical derivatives with fractional derivatives in the standard Newton root-finding method, using alternative iterations to the standard Picard iteration. By applying this process to polynomials on a complex plane, images known as polynomiographs are produced to show basins of attractions for polynomial zeros or the number of iterations required to achieve any polynomial root. The color coding of the images according to the number of iterations reveals the convergence speed and dynamic properties of the processes visualized by the polynomiographs. Additionally, the stability of the methods is investigated using basins of attraction, and a comparison of the modified root-finding methods is demonstrated on the polynomial z(3)-1 in a complex plane.
NUMERICAL ALGORITHMS
(2021)
Article
Mathematics, Applied
Haihong Guo et al.
Summary: This paper investigates the existence of chaos in a type of partial difference equations, and establishes four chaotification schemes using tangent and cotangent functions. The systems are shown to exhibit chaos in the sense of Li-Yorke or both Li-Yorke and Devaney. Three examples are provided for illustration.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics, Applied
Mudassir Shams et al.
Summary: Two new iterative methods have been established for the simultaneous determination of all multiple as well as distinct roots of nonlienar polynomial equations, with very high computational efficiency achieved using two suitable corrections. The convergence analysis shows that the orders of convergence of the newly constructed simultaneous methods are 10 and 12. Numerical test examples are provided to check the efficiency and numerical performance of these simultaneous methods.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics, Applied
Mudassir Shams et al.
Summary: This paper introduces a new numerical iterative scheme for estimating all roots of polynomial equations, which possesses 12th-order convergence locally according to convergence analysis. Numerical examples and computational cost are provided to demonstrate the capability of the proposed method.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics, Applied
A. Torres-Hernandez et al.
Summary: This paper introduces a method to accelerate the convergence speed of the fractional Newton-Raphson method, as well as how Aitken's method can speed up the convergence of iterative methods. Experimental results show that implementing Aitken's method in the F N-R method can lead to faster convergence compared to the simple F N-R method.
Article
Computer Science, Hardware & Architecture
Mudassir Shams et al.
Summary: This research article investigates two new modifications to the inverse Weierstrass iterative method, aiming to accelerate the convergence order to 3. Using computational algebra system and MATLAB, the efficiency and performance of the newly constructed methods have been validated and proven to be superior to existing inverse and classical simultaneous iterative methods.
COMPUTER SYSTEMS SCIENCE AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Nazir Ahmad Mir et al.
ALEXANDRIA ENGINEERING JOURNAL
(2020)
Article
Physics, Multidisciplinary
N. H. Tuan et al.
CHINESE JOURNAL OF PHYSICS
(2020)
Article
Mathematics, Applied
Ali Akgul et al.
APPLIED MATHEMATICS LETTERS
(2019)
Article
Mathematics, Applied
Gyurhan H. Nedzhibov
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
(2013)
Article
Mathematics, Applied
Xia Wang et al.
APPLIED MATHEMATICS LETTERS
(2010)
Article
Engineering, Electrical & Electronic
Pankaj Kumar et al.
