Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería / International Journal of Numerical Methods for Calculation and Design in Engineering

RIMNI - An International Journal of Numerical Methods for Calculation and Design in Engineering (Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería) is a peer-reviewed Open Access journal, founded in 1985. RIMNI publishes articles written in Spanish and English. The journal's scope includes Computational and Numerical Models of Engineering Problems, Development and Application of Numerical Methods, Advances in Software, Computer Design Innovations, Soft Computing, Machine Learning, Artificial Intelligence, etc. RIMNI is an essential ... show more

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Adaptive Power Splitting Strategies for Smart Microgrids with Enhancing Energy Efficiency and Resilience through Dynamic Load Management
A. Shaher, Z. Mushtaq, G. Abbas, H. Alwadie, M. Irfan, H. Murtaza, A. Shaheen, S. dawsari

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 41

Abstract
The integration of a renewable energy distributed generation into microgrids poses a significant constraint in the way power is managed, further so due to the natural variability in renewable generation and the variability in the load demands. To address these issues, this paper introduces a novel approach to the Spider Swarm Optimization (SSO) algorithm, the Dynamic LoadAdaptive Power Splitting (DLAPS) strategy, to enable real-time adaptive power sharing and enhance system resilience. Unlike the classical methods of power allocation that are static, according to which the power is divided between sources of renewable energy and storage systems, and between these sources and critical loads, the DLAPS-SSO applies the idea of a machine learning based predictive model to predict the power and dynamically optimize power allocation between the sources of renewable energy and storage systems and the sources and the critical loads. The model provides a multi-objective optimization framework that aims to minimize power losses and grid frequency variations, and to maximize the system’s resilience to disturbances, including disconnection from the grid, component malfunctions, and the availability of renewable energy sources. The comparison of simulation results with those of the Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) methods shows that the energy efficiency of the DLAPS-SSO increases by 15%–20%, and the amount of power losses across various load profiles decreases by 30%–35%. Moreover, the proposed solution offers 60% faster recovery time in case of grid disconnection, maintains 65.9% of the critical load in case of component failure, and provides 40%–50% less resilience than state-of-the-art techniques. The analysis of seasons and real data shows that there is stability of the behavior with the increase of efficiency (18%–22% during winter, and 23%–25% during summer), and the ability of the suggested approach to be robust when changing plant configuration/operation. Integration of optimization of dynamic load management and adaptive power splitting will spur microgrid control strategies and offer a viable strategy to stabilize the grid, reduce operation costs, and enable sustainable changes in energy transformations. The results demonstrate the essential role of bio-inspired optimization and reactivity in the next generation of smart grids.
Abstract
The integration of a renewable energy distributed generation into microgrids poses a significant constraint in the way power is managed, further so due to the natural variability [...]
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Advanced Computational Study of Nonlinear Time-Fractional Newell-Whitehead-Segel Equation with Caputo-Fabrizio Derivative Using B-Spline Techniques
M. Shafique, M. Yaseeen, S. Trabelsi, M. Balti

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 42

Abstract
This study presents numerical solutions for the time-fractional NewellWhitehead-Segel (NWS) equation with a Caputo-Fabrizio derivative. Spatial derivatives are discretized using three B-splines-cubic, cubic trigonometric and extended cubic B-splines-while temporal discretization is handled by a finite difference scheme. The proposed schemes are rigorously analyzed for stability and convergence. Their performance is evaluated in terms of accuracy and computational efficiency. Numerical experiments confirm the effectiveness of these techniques in capturing the dynamics of the fractional NWS equation. Each B-spline variant demonstrates unique strengths, highlighting the flexibility of B-spline approaches for solving fractional differential equations with nonlocal, memory-dependent operators. These results affirm the reliability and robustness of B-spline-based methods for such problems, paving the way for future advancements in this area.OPEN ACCESS Received: 23/08/2025 Accepted: 08/12/2025
Abstract
This study presents numerical solutions for the time-fractional NewellWhitehead-Segel (NWS) equation with a Caputo-Fabrizio derivative. Spatial derivatives are discretized [...]
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On a Class of Hybrid Langevin Inclusions Involving Two Generalized Fractional Derivatives
A. Lachouri, M. Arab

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 60

Abstract
In this paper, we study the existence of solutions for a hybrid Langevin inclusion involving a combination of φ-Hilfer and φ-Caputo fractional derivatives. To this end, we construct a new operator derived from the integral solution of the given boundary value inclusion problem and subsequently apply the hypotheses of Dhage’s fixed point theorem to this fractional operator. Finally, to support our theoretical findings, an illustrative example is provided.OPEN ACCESS Received: 13/11/2025 Accepted: 20/01/2026
Abstract
In this paper, we study the existence of solutions for a hybrid Langevin inclusion involving a combination of φ-Hilfer and φ-Caputo fractional derivatives. To this [...]
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Advancing Fractional Calculus: A Fixed-Point Strategy for Nonlinear Caputo-Hadamard Equations
M. Awadalla, M. MURUGESAN

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 62

Abstract
This paper investigates the existence, uniqueness, and Ulam–Hyers stability of solutions for a coupled system of nonlinear Caputo–Hadamard fractional differential equations in Banach spaces. By reformulating the boundary value problem into an equivalent integral system via the Hadamard fractional integral operator, sufficient conditions for existence and uniqueness are established using Krasnoselskii’s and Banach’s fixedpoint theorems. Within the same functional framework, Ulam–Hyers stability results are derived for the proposed system. The theoretical analysis provides a consistent and unified approach for studying nonlinear coupled fractional systems with nonlocal operators, and the validity of the assumptions is illustrated through representative examples.
Abstract
This paper investigates the existence, uniqueness, and Ulam–Hyers stability of solutions for a coupled system of nonlinear Caputo–Hadamard fractional differential [...]
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Garhy distribution with Different Estimation Methods and Applications to Engineering and Medical Data
M. Elgarhy

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 61

Abstract
In this article, we introduce and investigate a new one-parameter mixture distribution called the “Garhy distribution”. The probability density function is very adaptable, as it may take on right skewed, unimodal, and heavy tailed patterns. In addition, the hazard rate function indicates that data with increasing shaped failure rates may be adapted by the Garhy distribution. Several fundamental statistical and mathematical properties are calculated including mode, quantile function, moments, mean, variance, skewness, kurtosis, moment-generating function, incomplete moments, inequality measures, order statistics, and extropy measures. The scale parameter of the Garhy distribution is estimated employing twelve different estimation approaches, maximum likelihood, maximum product of spacings, least-squares, weighted least-squares, Anderson darling, right-tail Anderson darling, left-tail Anderson darling, Cramér von-Misses, and the least-squares method. The effectiveness of these strategies is evaluated using a detailed simulation study. Furthermore, we used the Garhy distribution to examine two real-world data sets, demonstrating its superior performance compared to specific competitors.
Abstract
In this article, we introduce and investigate a new one-parameter mixture distribution called the “Garhy distribution”. The probability density function is very [...]
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