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This paper focuses on developing and analyzing a new AR-iterative scheme designed for estimating fixed points of generalized non-expansive mappings of the Suzuki kind. The scheme’s stability and convergence properties are rigorously proven, highlighting its superior convergence rate for non-expansive mappings when compared to existing schemes in the literature. Additionally, an application of the AR-iterative scheme to differential equations is presented. These findings underscore the effectiveness and versatility of the proposed scheme in numerical analysis and computational mathematics. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a novel approach for estimating the fixed points of multi-valued non-expansive mappings using the AR-iteration scheme in the context of uniformly convex Banach spaces. We establish strong and weak convergence results, providing rigorous analytical proofs and illustrating the results with a detailed example. Our approach showcases the potential of the AR-iteration scheme in solving real-world problems, particularly in addressing two-point boundary value problems. We demonstrate the applicability and effectiveness of the AR-iteration scheme in numerical analysis and computational mathematics. Our results contribute significantly to the advancement of numerical methods in solving boundary value problems, offering new insights and directions for future research in this area. Furthermore, we provide a detailed explanation of Green’s function approach and its implications for various scientific and engineering applications, paving the way for future research in this area. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical solution of the time-fractional Gilson–Pickering equation using the Kansa method, in which the multiquadrics were utilized as the radial basis function. To achieve this, a meshless numerical scheme based on the finite difference along with the Kansa method has been presented. First, the finite difference approach has been utilized to discretize the temporal derivative, and subsequently, the Kansa method is employed to discretize the spatial derivatives. The stability and convergence analysis of the numerical scheme are also elucidated in this paper. Furthermore, the soliton solutions have been acquired by implementing the Kudryashov method for comparison with the numerical results. Finally, numerical simulations are performed to confirm the applicability and accuracy of the proposed scheme. [ABSTRACT FROM AUTHOR]

Memristor, as a nonlinear element, provides many advantages thanks to its superior properties to design different chaotic circuits. Thus, a novel four-dimensional double-scroll chaotic system with line equilibria as well as two unstable equilibria based on the flux-memristor model is proposed in this paper. The effects of initial values and parameters on the dynamic characteristics of the system are studied in detail by means of phase diagrams, Lyapunov exponent spectrums, bifurcation diagrams, two-parameter bifurcation diagrams and basins of attraction. Besides, a series of complex phenomena in the system, such as sustained chaos, bistability, transient chaos and coexisting attractors are observed, proving that the chaotic system has rich dynamic characteristics. Also, spectral entropy (SE) complexity algorithm and C 0 complexity algorithm based on structure complexity are adopted to analyze the complexity of the system. Additionally, PSPICE circuit simulation and Micro-Controller Unit (MCU) hardware experiment are carried out to verify the correctness of theoretical analysis and numerical simulation. Finally, the pulse chaos synchronization is achieved from the perspective of maximum Lyapunov exponent, and numerical simulations demonstrate the occurrence of the proposed system and practicability of the pulse synchronization control. [ABSTRACT FROM AUTHOR]