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166 articles for “Kuramoto–Sivashinsky equation”
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Exact Solutions of Kuramoto–Sivashinsky Equation Using Modified Sub-equation Method
Abstract: Equations for non-linear evolution are mathematical representations of physical phenomena. The physical interpretation of the solution functions of these equations enhances the viewpoint of many natural processes. Numerous scientists who acknowledge this truth have focused on this area. These mathematical models are even more important since they provide light on a multitude of events when their solutions take on a physical significance. Through their research, numerous scientists create methods and …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 2, 2024 · pp. 25–33 Read article
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Differential Equations in Quantum Mechanics and Schrödinger Equation
Abstract: In this study we investigate how differential equations play a role in quantum mechanics, focusing mainly on the role of a prominent one, Schrödinger's equation, which governs the behavior of quantum systems. In time two the mathematical picture of the wave nature of particles at quantum scales is provided, and the resulting equations are Schrödinger's equation, both in its time dependent as well as in its time independent form. The …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 1, 2025 · pp. 15–25 Read article
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Numerical Solution of Ordinary Differential Equation and Solution of Partial Differential Equation
Abstract: This research paper explores the fundamental role of various mathematical concepts in engineering and scientific fields like aerospace engineering, materials science, software development, and the energy sector. We delve into the applications of solving algebraic and transcendental equations, finite difference interpolation, numerical methods, solutions to ordinary differential equations (ODEs), and numerical solutions to partial differential equations (PDEs). By examining their applications in these diverse fields, we illustrate the critical importance …
Published in Journal of Aerospace Engineering & Technology · Vol. 14, Issue 3, 2024 · pp. 12–20 Read article
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From Differential Equations to Data Science: A Survey on Analytical Methods in Contemporary Problems
Abstract: The integration of differential equations and data science methods represents a dynamic and evolving approach to solving contemporary challenges across a wide range of disciplines, including engineering, physics, biology, economics, and finance. Differential equations have long served as fundamental tools for modeling continuous systems and processes, offering powerful insights into the behavior of natural and man-made phenomena. For example, they describe how heat diffuses through materials, how populations grow in …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 1–6 Read article
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Advance Fixed Point Theorems and Its Application to Ordinary and Fractional Differential Equations
Abstract: In the present research, advanced results on the fixed point theorem are applied to typical boundary value problems. Finding a differential equation's solution under certain boundary conditions is the goal of typical boundary value topics. The article appears to extend new fixed point results to a new context, likely involving fractional operators with unique kernels, notably the Caputo-type fractional operator. This extension involves applying the fixed point theorem to a …
Published in Recent Trends in Mathematics · Vol. 1, Issue 1, 2024 · pp. 1–15 Read article
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Key Generation Algorithms Using Difference Equations with Multi-Precision Arithmetic: A Review
Abstract: Modern cryptographic systems rely on robust key generation to secure data and communication. This review explores the integration of difference equations and multi-precision arithmetic for cryptographic key generation, addressing limitations in traditional methods like pseudorandom number generators and chaotic systems. Difference equations produce deterministic yet chaotic sequences ideal for cryptography due to their sensitivity to initial conditions and nonlinearity. However, finite precision arithmetic can lead to periodicity and loss of …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 3, 2024 · pp. 23–36 Read article
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Optimal Homotopy Analysis Method (OHAM) For the Approximate Series Solution of Non-linear Partial Differential Equation
Abstract: In this article, we have used the Optimal Homotopy Analysis Method (OHAM), which is a basically semi-analytic method to solve differential equations. The ability for the user to choose the convergence control parameter, auxiliary linear operator, auxiliary function, and starting approximation is what sets apart the OHAM technique. We guaranteed the efficacy and efficiency of the procedure by fine-tuning the convergence control parameter. We solved a non-linear partial differential equation …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 1, 2024 Read article
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Mathematical Modeling of Epidemics Using Stochastic Differential Equations: A Review
Abstract: The accurate modeling of infectious disease dynamics is crucial for predicting outbreaks and informing public health interventions. While deterministic models such as the SIR (Susceptible-Infected-Recovered) framework have traditionally been used to understand disease transmission, they often fail to account for the randomness inherent in real-world scenarios. Disease spread is influenced by numerous uncertain factors, including individual behavioral changes, environmental fluctuations, and imperfect data reporting. These uncertainties can significantly impact model …
Published in Recent Trends in Mathematics · Vol. 1, Issue 2, 2024 · pp. 1–6 Read article
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Real-Time Edge Detection Camera Module Using Discrete Taylor Transform and Heat Equation (PDE): An Applied Mathematical Approach
Abstract: In modern digital signal processing, the capability for denoising and smoothing in real time is very important in scientific, engineering, and industrial applications. This paper presents an efficient hybrid framework that merges two mathematically sound methods, namely, DTT and PDE defined as the Heat Equation, to robustly denoise a signal with minimal distortion. The model addresses one of the most challenging tasks in signal restoration, which maintains the fidelity of …
Published in Current Trends in Signal Processing · Vol. 16, Issue 2, 2026 Read article
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Study on the Method of Constructing a System of Linear Equations for Calculating Aerodynamic Derivatives
Abstract: The aerodynamic derivatives can be calculated from the unsteady hydrodynamic forces experienced by the harmonic-oscillating vehicle. Until now, unsteady flow field analysis in aerodynamic derivative calculations has been applied mainly to thin bodies based on potential theory MSC. Nastran is a typical application based on potential theory MSC. Natran can calculate the aerodynamic derivatives of the vehicle relatively well in the subsonic region, but in the supersonic region, the fuselage …
Published in Journal of Experimental & Applied Mechanics · Vol. 16, Issue 3, 2025 · pp. 14–24 Read article
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Effect of hybrid plant-based cutting fluid in turning operation of EN19 steel and modelling of heat transfer equation for multiple phase colloids
Abstract: This article describes a project where an alternative to conventional Mineral Oil (MO) based cutting fluids is tried on the turning operation of steel samples. The deposit of petroleum is getting depleted day by day, the pollution due to fossil fuel is increasing exponentially and petroleum is getting more and more expensive. Due to these reasons, nonpetroleum (MO) based alternative cutting fluids have been in business for quite a while. …
Published in Journal of Polymer & Composites · Vol. 11, Issue 12, 2023 · pp. 175–185 Read article
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Agentic AI: Architectures, Types, Capabilities, Mathematical Equations and Governance in the Era of Autonomous Intelligence
Abstract: Agentic Artificial Intelligence (Agentic AI) represents a major advancement in the evolution of intelligent systems by enabling autonomous planning, decision-making, and action execution. Unlike traditional AI models, which are primarily reactive and designed to respond to predefined inputs, Agentic AI systems possess capabilities such as memory, reasoning, goal-oriented planning, tool integration, and dynamic adaptation to changing environments. These characteristics allow them to perform complex, multi-step tasks with minimal human intervention, …
Published in Recent Trends in Mathematics · Vol. 3, Issue 2, 2026 Read article
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Study on the Variations in Physicochemical Property Concentration in a Contaminated Fresh and Salt Water
Abstract: In this research, the dispersion of crude oil contaminated was subjected into laboratory observations and results were recorded. These results were used to develop and adopt mathematical models for a proper engineering experimental practice. 1.5m3 volumes of fresh water and salt water were filled in two tanks of equal fit at the same intervals along the tanks and depth, where samples were collected for the purpose of analysis of physicochemical …
Published in International Journal of Pollution: Prevention & Control · Vol. 1, Issue 2, 2023 · pp. 1–9 Read article
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Seismic Hazard Evaluation through Attenuation Law Derivation and Response Spectrum Design: Bangladesh Case Study
Abstract: Bangladesh, positioned at the confluence of the Indian, Eurasian, and Burma tectonic plates, faces significant seismic hazards due to its complex geological setting. This research focuses on formulating empirical attenuation relationships and Creating a design response spectrum for assessing seismic risks in Bangladesh, using data from ten large earthquakes with magnitudes ranging from 6. 7 to 7. 9. The study creates Ground Motion Prediction Equations (GMPEs) for various structural periods …
Published in Journal of Structural Engineering and Management · Vol. 12, Issue 3, 2025 · pp. 54–63 Read article
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Numerical Simulation of Transient Free Convection in a Rectangular Cavity Filled with Porous Material Using Finite Element Formulations
Abstract: In this study, the finite element method is used to quantitatively explore transient free convection in porous cavities in order to understand the flow characteristics and heat conduction processes in the square cavities. In comparison to an uniform temperature gradient, the left wall is swiftly heated and the right wall is allowed to cool to a specific temperature. The horizontal walls are insulated on both sides. Dimensionless representations of the …
Published in Journal of Polymer & Composites · Vol. 11, Issue 8, 2023 · pp. 1–10 Read article
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Mathematical Modelling of Semiconductor Device Physics: An Analytical Approach
Abstract: Semiconductor device physics forms the foundation of modern electronic and optoelectronic technologies. Mathematical modelling provides a rigorous framework for understanding, predicting, and optimizing the behavior of semiconductor devices by linking physical principles with device-level performance. This work presents an analytical approach to the mathematical modelling of semiconductor devices, emphasizing the derivation and interpretation of governing equations that describe charge transport and electrostatic behavior. The model is based on fundamental physical …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 13, Issue 1, 2026 · pp. 36–42 Read article
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Effect of Initial Temperature and Diameter of Ethanol Droplet on Evaporation Dynamics in Convective Air Medium
Abstract: Ethanol is a suitable biofuel as it has fewer toxic emissions and higher-octane numbers. For spray combustion applications, the gas phase motion must be considered while numerically investigating the fundamental aspects of droplet evaporation and combustion processes. Hence, we have numerically simulated the evaporation dynamics of an isolated spherically shaped ethanol droplet under a forced convective air environment in the absence of gravity. The momentum transfer between two phases is …
Published in Journal of Polymer & Composites Read article
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Time and Frequency Response of Non-uniform Overhead Lines Under Corona
Abstract: This study presents an efficient and direct technique for determining both the time and frequency responses of non-uniform overhead power transmission lines operating under corona conditions. The assumed-line's non-uniformity is due to the conductors’ sag. Expressions will be presented for the location-dependent line surge impedance and the unevenly distributed lines’ electrical parameters. The analysis starts with solving the relevant system of differential and algebraic equations, subject to the boundary conditions. …
Published in International Journal of Electrical Machine Analysis and Design · Vol. 2, Issue 2, 2024 · pp. 25–33 Read article
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Analysis of Field Distribution in Optical Fibre Using FEM Method
Abstract: The application of the linear Finite Element Method (FEM) to the analysis of the field distribution in optical fibres is examined in this work. Characterizing fibre characteristics like mode profiles, propagation constants, and dispersion, all of which are critical for maximizing fibre performance in a variety of applications like sensing and telecommunications, requires an understanding of the distribution of electric and magnetic fields. In order to accurately determine the modal …
Published in Trends in Opto-electro & Optical Communication · Vol. 15, Issue 2, 2025 · pp. 31–40 Read article
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Revolutionizing Optical Fibre Field Distribution with Linear Finite Element Method
Abstract: This study investigates the use of the linear Finite Element Method (FEM) for the analysis of the field distribution in optical fibres. Understanding the distribution of electric and magnetic fields is necessary to characterise fibre properties including mode profiles, propagation constants, and dispersion, all of which are essential for optimising fibre performance in a range of applications like sensing and telecommunications. This study emphasises on applying a linear FEM formulation …
Published in Trends in Opto-electro & Optical Communication · Vol. 15, Issue 3, 2025 · pp. 32–42 Read article