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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]

This contribution discusses the influence of different barrier update strategies on the performance and robustness of an interior point algorithm for single-crystal plasticity at small strains. To this end, single-crystal plasticity is first briefly presented in the framework of a primal-dual interior point algorithm to outline the general algorithmic structure. The manner in which the barrier parameter is modified within the interior point method, steering the penalization of constraints, plays a crucial role for the robustness and efficiency of the overall algorithm. In this paper, we compare and analyze different strategies in the framework of crystal plasticity. In a thorough analysis of a numerical example covering a broad range of settings in monocrystals, we investigate robust hyperparameter ranges and identify the most efficient and robust barrier parameter update strategies. [ABSTRACT FROM AUTHOR]

This work explores a well-established eighth-algebraic-order numerical method belonging to the explicit Numerov-type family. To enhance its efficiency, we integrated a cost-effective algorithm for adjusting the step size. After each step, the algorithm either maintains the current step length, halves it, or doubles it. Any off-step points required by this technique are calculated using a local interpolation function. Numerical tests involving diverse problems demonstrate the significant efficiency improvements achieved through this approach. The method is particularly effective for solving differential equations with oscillatory behavior, showcasing its ability to maintain high accuracy with fewer function evaluations. This advancement is crucial for applications requiring precise solutions over long intervals, such as in physics and engineering. Additionally, the paper provides a comprehensive MATLAB-R2018a implementation, facilitating ease of use and further research in the field. By addressing both computational efficiency and accuracy, this study contributes a valuable tool for the numerical analysis community. [ABSTRACT FROM AUTHOR]

This paper proposes an L1/LDG algorithm for a time–space fractional convection equation on a bounded rectangular domain Ω⊂ℝ2$$ \Omega \subset {\mathrm{\mathbb{R}}}^2 $$. Here, the temporal partial derivative is in the sense of Caputo with order α∈(0,1)$$ \alpha \in \left(0,1\right) $$, and the spatial partial derivatives are of Riesz type with orders β,γ∈(0,1)$$ \beta, \gamma \in \left(0,1\right) $$ in x$$ x $$‐ and y$$ y $$‐directions, respectively. L1 approximation is utilized to evaluate the temporal Caputo derivative, while the local discontinuous Galerkin (LDG) method is adopted to deal with the spatial Riesz derivative. The rigorous numerical stability analysis and error estimate are presented which are supported by illustrative numerical examples. [ABSTRACT FROM AUTHOR]

This paper proposes a cooperative pursuit strategy against a maneuvering target by introducing a cascaded optimization framework for assignment and guidance. The cooperative guidance algorithm, guaranteeing both encirclement and simultaneous attack constraints, is derived by optimizing the normal impact–direction and tangential impact–time control efforts, respectively. Then, by minimizing the performance index identical to the guidance loop, an assignment approach is proposed to allocate the desired impact direction and time for each pursuer. Since the assignment and guidance strategies share a unified optimization tenet in a cascaded manner, the proposed integrated cooperative method proves more efficient than the existing guidance-only methods. Theoretical analysis and numerical simulations are provided to demonstrate its advantages in synergy efficiency. [ABSTRACT FROM AUTHOR]

• Numerical methods used for the estimation of the RMS. • Simpson's 1/3 rule and Simpson's 3/8 rule modified for the purpose of general application. • Modified Simpson's rules do not necessitate more complex mathematical calculations than those used in the existing methods. • Modifications provide better measurement results for some a lower ratio of the frequency of sampling and the frequency of the signal. • Modified methods do not require the manufacturers of commercial measurement equipment to additionally invest in it. This paper demonstrates that direct changes in the algorithm for the estimation of the root mean square value of a voltage signal of an arbitrary waveform can lead to improved performances and lower measurement uncertainty of commercially available instruments without requiring any upgrade of their existing hardware. The research conducted and presented here is an original contribution to the development of estimation techniques and mathematical models for measurement oriented purposes regardless of the number of samples in the given period relying on mathematical calculation of the equal complexity as in the methods already in use. The theoretical approach examines the problem of numerical integration focusing on modified Simpson's 1/3 rule and modified Simpson's 3/8 rule used for the purpose of the estimation of the root mean square value when a small number of samples per period is available. It highlights the limitations of Simpson's 1/3 rule and Simpson's 3/8 rule, and shows that the newly proposed algorithm is optimal with respect to measurement accuracy and precision even in cases when the ratio of the sampling frequency and the signal's fundamental frequency is low. All theoretical results have been validated experimentally. [ABSTRACT FROM AUTHOR]