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61 articles for “difference equations”
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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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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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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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The Electromagnetic Transients in Compensated High Voltage Power Lines
Abstract: This paper addresses the simulation of the transients developed in high voltage lines, which are initiated by lightning discharges. The analysis allows for compensated and uncompensated lines. Both the individual and simultaneous series inductive and shunt capacitive compensation types can be dealt with. The sizes and locations of the compensating elements are included in the analysis. Numerous studies on the transient concentrated stresses across these elements and the related protection …
Published in International Journal of Electrical Power and Machine Systems · Vol. 1, Issue 2, 2023 · pp. 1–8 Read article
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Land surface dynamics: A Multiphysics Approach to Modeling Mass Transport
Abstract: Land surface dynamics are governed by complex interactions among hydrological, atmospheric, and geomorphological processes that collectively drive the transport of mass across terrestrial environments. Traditional modeling approaches often isolate individual mechanisms, limiting their ability to capture the coupled feedbacks that shape landscape evolution. This study presents a multiphysics framework for modeling mass transport on land surfaces, integrating fluid flow, sediment transport, heat exchange, and chemical reactions within a unified computational …
Published in International Journal of Land · Vol. 2, Issue 2, 2025 · pp. 31–36 Read article
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The Rise of Fractional Calculus: Novel Applications in Engineering and Biological Systems
Abstract: Fractional calculus (FC) is an advanced mathematical framework that generalizes the classical concepts of differentiation and integration to non-integer, or fractional, orders. This extension of traditional calculus allows for the modeling of complex dynamic systems that exhibit behavior not easily captured by integer-order differential equations. Over the last few decades, fractional calculus has seen a rapid rise in popularity, particularly in applied mathematics, engineering, and biological sciences, due to its …
Published in Recent Trends in Mathematics · Vol. 1, Issue 2, 2024 · pp. 7–11 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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Direct Determination of the Frequency-Dependent Transmission Constants of Non-Uniform Two-Port Networks
Abstract: Due to space constraints and the expansion of electricity networks, transmission lines that cross close to one another are now commonplace. Power networks also commonly install higher operational voltage lines that share transmission corridors with lower voltage lines. Overhead transmission lines are the primary method for transmitting electrical energy across vast distances. This paper presents an efficient and direct technique for identifying the four frequency-dependent ABCD transmission constants of arbitrary …
Published in Journal of Power Electronics and Power Systems · Vol. 14, Issue 3, 2024 · pp. 1–8 Read article
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Electromagnetic Transients in Compensated Overhead Lines with Multiple Tower Spans
Abstract: This paper addresses the analysis of the electromagnetic transients developed in an important class of non-uniform high-voltage power lines. It deals particularly with compensated long overhead high- voltage transmission lines composed of several tower spans, which are connected in cascade. The derived mathematical model leads to a system composed of simultaneous partial differential and algebraic equations, which can be solved numerically in terms of parametric functions using the software Mathematica’s …
Published in Trends in Electrical Engineering · Vol. 15, Issue 2, 2025 · pp. 1–9 Read article
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Analyzing The Electromagnetic Transients and Corona Performance of Long Overhead Lines with Multiple Tower Spans
Abstract: This paper addresses the simulation of the electromagnetic transients developed in an important class of non-uniform high voltage power lines. The resulting information is of paramount importance for the proper planning, design, operation and protection of electric power networks. It deals particularly with long overhead high voltage transmission lines composed of several tower spans which are connected in cascade. The presented approach considers eventually existing localized corona discharges at some …
Published in International Journal of Electrical and Communication Engineering Technology · Vol. 3, Issue 1, 2025 · pp. 35–44 Read article
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Differential Model of Wave Vibration on Strings and Rods
Abstract: Vibration, as a physical phenomenon, plays a multifaceted role in both natural and engineered systems. Beyond its essential contribution to communication through sound and speech, it finds critical application in various technological domains. For instance, in the design of stringed musical instruments such as violins and guitars, precise manipulation of string vibrations defines tonal quality and musical resonance. Similarly, metal rods in tuning forks exhibit vibrational properties that are finely …
Published in Research & Reviews : Journal of Physics · Vol. 14, Issue 1, 2025 · pp. 17–21 Read article
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Modeling of MHD Hybrid Nanofluid Flow with Radiation and Chemical Reaction Effects for Advanced Composite and Energy Applications
Abstract: Hybrid nanofluids reinforced with polymer-based matrices and nanoparticles have emerged as promising working fluids for advanced composite processing and thermal management systems. Their superior thermo-physical properties enable efficient cooling and energy transport, making them suitable for applications in polymer extrusion, composite curing, thermal insulation coatings, solar energy devices, electronic packaging, and nuclear system cooling. In this study, we investigate the heat and mass transfer behavior of magnetohydrodynamic (MHD) hybrid nanofluid …
Published in Journal of Polymer & Composites · Vol. 14, Issue 1, 2026 · pp. 648–660 Read article
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Fractional Calculus-Based Analysis of Magneto-Thermal Nanofluid Flow Over Stretching and Shrinking Surfaces
Abstract: This study presents a comprehensive investigation of magneto-thermal hybrid nanofluid flow over stretching and shrinking surfaces using a fractional calculus framework to capture the memory and hereditary characteristics of complex fluid transport phenomena. The proposed model incorporates the effects of magnetic field intensity, thermal radiation, viscous dissipation, Brownian motion, and thermophoretic diffusion on the velocity and temperature distributions within the boundary layer region. A fractional-order derivative formulation is employed to …
Published in Recent Trends in Fluid Mechanics · Vol. 13, Issue 2, 2026 Read article
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Harmonically Varying Moving Load on Time-Dependent Uniform Beam Resting on Pasternak Foundation
Abstract: In this paper, we investigated elastic beam whose properties does not varies with spatial coordinate but constant along the span L of the beam. The moving load considered in this work is harmonically varying moving load with non-classical boundary conditions, time dependent boundary conditions in particular. Also, considered in this work is two parameters foundation which are Winkler and Pasternak foundations. Closed form solutions in plotted form are obtained using …
Published in International Journal of Electro-Mechanics and Material Behaviour · Vol. 3, Issue 2, 2025 · pp. 38–47 Read article
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Coupled Magneto–Thermal–Diffusion Transport in an Unsteady Maxwell Polymer Fluid with Activation Energy over a Porous Stretching Surface
Abstract: The present study investigates the combined effects of activation energy and diffusion-thermo (Dufour) processes on unsteady magnetohydrodynamic (MHD) flow, heat, and mass transfer of a Maxwell viscoelastic fluid past a porous exponentially stretching vertical sheet. The electrically conducting and incompressible polymeric fluid flows through a saturated porous medium under a transverse magnetic field. The governing momentum, energy, and concentration equations are transformed into nonlinear ordinary differential equations using similarity transformations …
Published in Journal of Polymer & Composites · Vol. 14, Issue 1, 2026 · pp. 581–590 Read article
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Modeling and Simulation of Radiative MHD Casson-Type Polymer Composite Flow over a Porous Wedge with Variable Thermal Source and Sink
Abstract: This study presents a numerical investigation of the radiative magnetohydrodynamic (MHD) flow and heat transfer characteristics of a Casson-type polymer fluid over a moving and extending porous wedge under the influence of a spatially varying heat source and sink. The Casson fluid model, representing a class of viscoplastic polymeric materials, is analyzed within the MHD framework to explore the combined effects of magnetic field intensity, rheological behavior, and porous medium …
Published in Journal of Polymer & Composites · Vol. 14, Issue 1, 2026 · pp. 837–850 Read article