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16 articles for “partial differential 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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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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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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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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CFD Analysis of Six-Flow Microchannel Heat Sink Using the Different Nanofluid
Abstract: In this study, we compare the heat-conveying capabilities of ordinary water with those of cooling fluids such as Ag-Water, TiO2-water, and Al2O3-water nanofluid at a volume percentage of 0.50%, and we also examine the six flow micro-channels of the fin-equipped heat sink. Hardware like microprocessors and integrated circuits are not used in the comparison. To evaluate the effectiveness of different cooling fluids, a number of thermal metrics are used, such …
Published in Journal of Polymer & Composites · Vol. 11, Issue 11, 2023 · pp. 1–11 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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Strategic Solutions: How Mathematics Reshapes Industrial Landscapes
Abstract: One of the earliest and most fundamental fields of the physical sciences is mathematics. It has a significant impact on industrial enterprises' bottom lines and enhances their performance in the current data-driven market. One subfield of applied mathematics is industrial mathematics. It concentrates on issues that arise in the industry and seeks answers that are pertinent to the sector. The use of mathematical models and techniques to diverse industry difficulties …
Published in International Journal of Industrial and Product Design Engineering · Vol. 2, Issue 1, 2024 · pp. 16–23 Read article
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Electromagnetic Transients in Strongly Non-Uniform Overhead High Voltage Lines
Abstract: This paper addresses the electromagnetic transients in high strongly non-uniform overhead voltage lines. For their simulation, a novel Laplace-domain approach has been introduced. The voltage and current patterns in terms of location and complex frequency are determined by a set of simultaneous algebraic and partial differential equations. To solve them numerically, an effective Mathematica code is proposed. By contrasting the outcomes of their application to multiple case studies with those …
Published in Journal of Power Electronics and Power Systems · Vol. 15, Issue 1, 2025 · pp. 30–36 Read article
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Inverse Model for Predicting Thermal Abnormality of the Transient Process Triggered by Defective Electronics Element
Abstract: The paper presents a model for predicting thermal abnormalities in Printed Circuit Boards (PCBs) by approximating the thermal process of electric elements with heating from point sources. Circuit board heat sources are defined as point and non-point. The point heat source is a small electronic heating element that can be approximated as having originated from one point on the circuit board. A non-point source is one with heat distributed over …
Published in International Journal of Energy and Thermal Applications · Vol. 3, Issue 2, 2025 · pp. 24–31 Read article
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Flexural Vibration of Non-Uniform Beam on Bi-Parametric Foundation Under Harmonic Moving Load with Non-Classical Boundary Conditions
Abstract: The dynamic response to harmonically varying moving loads of non-uniform elastic beam resting on bi-parametric foundation with non-classical boundary condition, time dependent in particular is examined in this paper. Here, the beam is considered non-uniform, with the moment of inertia and the distributed mass varying continuously along the span L as functions of the position 𝑥. In order to guarantee a more stable structure and a reduce risk of resonance, …
Published in International Journal of Mechanical Dynamics and Systems Analysis · Vol. 3, Issue 2, 2025 · pp. 28–42 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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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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Quasar: Quantum-Accelerated Sustainable Anomaly Recognition in Climate Systems
Abstract: Accurate detection of climate anomalies is vital for disaster alleviation and policy making in a sustainable manner, but customary detection methods face the challenges of computational inefficiency and physical inconsistency. In this study, we propose a novel approach called Quantum-Optimized Fuzzy Physics-Informed Neural Networks (QFuzzy-PINNs), which integrates quantum computing, fuzzy logic, and physics-informed deep learning. As a first step, we employ quantum annealing for conventional optimization to adjust multiple Gaussian …
Published in International Journal of Climate Conditions · Vol. 2, Issue 2, 2025 · pp. 18–27 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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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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A Sustainable EOQ Model for Declining Products Incorporating Cubic Demand, Variable Deterioration, Partial Backlogging, and Carbon Emission Optimization
Abstract: In this paper proposes a sustainable Economic Order Quantity (EOQ) model for inventory systems involving decaying items under cubic time-dependent demand, variable decaying rates, and partial backlogging while absolutely considering carbon emission costs. The model reflects practical market actions where demand initially increases and afterwards declines over time, and decay depends on the age of the item. To demonstrate the current model's applicability as well as evaluate the trade-off between …
Published in International Journal of Industrial and Product Design Engineering · Vol. 4, Issue 1, 2026 · pp. 20–28 Read article