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11 articles for “approximate analytical solution”
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Fractional Homotopy Analysis Transform Method for a Fin Having Temperature Dependent Internal Heat Generation
Abstract: Fractional Homotopy Analysis Transform Method (FHATM) is a new analytical tool for solving homogeneous and non-homogeneous fin equations. FHATM is a novel and innovative modification in Laplace Transform Algorithm (LTA) thus making analysis easier. Non-linear problems are solved by proposed technique without using Adomian and He’s polynomial which is a clear benefit of this new algorithm over decomposition and homotopy perturbation transform methods. This is an elementary technique which gives …
Published in Journal of Experimental & Applied Mechanics · Vol. 10, Issue 1, 2019 · pp. 23–34 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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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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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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Power and Area - Aware Recursive Multiplier Architecture Utilizing Polymer Composites for Neural Network Acceleration
Abstract: Approximate computing is widely applied in error - tolerant systems as an effective technique to enhance circuit performance by deliberately allowing occasional inaccuracies instead of strictly ensuring precise results for every computation. Among the fundamental building blocks of digital systems, multipliers play a crucial role in signal processing, control systems, and machine learning applications; however, they demand significant power, silicon area, and timing resources. Leveraging error - tolerant approximate multipliers …
Published in Journal of Polymer & Composites · Vol. 14, Issue 1, 2026 · pp. 1320–1337 Read article
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Mathematical Approaches to Nonlinear Oscillatory Systems with Damping: Exact and Approximate Solutions
Abstract: The study of nonlinear oscillatory systems with damping is a key area of research in applied mathematics, particularly in the context of dynamical systems, stability analysis, and bifurcation theory. These systems, described by second-order nonlinear differential equations, exhibit a rich variety of behaviors, including periodic, quasi-periodic, and chaotic motions. The introduction of damping—representing energy dissipation—adds a layer of complexity, making the analytical and numerical solution of such systems a challenging …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 7–11 Read article
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Stress Analysis and Deflection of Longitudinal Beam and Validate by using ANSYS
Abstract: This study investigates the deflection and stress distribution in a long, slender longitudinal beam of uniform rectangular cross section made of linear elastic material properties that are homogeneous and isotropic. The deflection of a longitudinal beam is essentially a three dimensional problem. An elastic stretching in one direction is accompanied by a compression in perpendicular directions. The beam is modeled under the action of three different loading conditions: vertical concentrated …
Published in Trends in Machine design · Vol. 7, Issue 1, 2020 · pp. 4–8 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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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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Analysis of Simply Supported and Clamped-Clamped Beam Resting on a Pasternak Foundation Subjected to Moving Load with a Damping Term
Abstract: A comparative analysis of simply supported and clamped-clamped Bernoulli-Euler beams resting on a Pasternak foundation under the action of a concentrated moving load with a damping term, when the inertia effect of the moving load is considered in its analysis, was investigated in this study. The governing equation was solved by representing the Dirac delta function through a Fourier cosine series and applying a combination of analytical techniques, including the …
Published in Journal of Experimental & Applied Mechanics · Vol. 16, Issue 3, 2025 · pp. 42–59 Read article
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Heavy Metal Removal from Textile Industrial Effluent using Banana Exocarp Derived Cellulose Acetate Graphene Nanocomposite Membranes
Abstract: The disposal of textile effluent is responsible for serious human health concerns and above all environmental concerns to all kind of species. This indicates that there is immediate and urgent need of emerging, efficient with sustainable recycling technologies. In this paper, banana exocarp as agriculture-based waste, in terms of substrate was utilised as major raw material. The extracted cellulose from the substrate with homogeneous acetylation process, transformed into cellulose acetate …
Published in Journal of Polymer & Composites · Vol. 14, Issue 4, 2026 · pp. 51–62 Read article