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606 articles for “Navier–Stokes 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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On the Universal Equation of Elasticity and the Universal Equation of Thermo-elasticity for Next-generation Aircrafts and Spacecrafts
Abstract: In the present investigation, the theories of “Relativistic Elasticity” and “Relativistic Thermo-Elasticity” are proposed for the design of the new-generation large aircraft with turbojet engines and speeds in the range of 50,000 km/h and for the new-generation spacecraft of any speed. Such theories show that there is a considerable difference between the absolute stress tensor and the stress tensor of the moving frames even in the range of speeds of …
Published in Journal of Aerospace Engineering & Technology · Vol. 2, Issue 1, 2012 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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The Milklipidometric Model: A Mathematical Equation-based on Electric Conductivity to Predict Butterfat Concentrations in Bovine Milk
Abstract: The milklipidometric model is a mathematical equation to predict butterfat in raw milk and it is based on electric conductivity principle. The model differs from the existing equations in that it uses variables (electric conductivity, and volume fraction of whole milk ) which can be easily measured and it predicts fat at wide temperature, range of 5–60°C. Accurate results can be obtained even using commercial electrical conductivity meters, hence making …
Published in Research and Reviews : Journal of Dairy Science and Technology · Vol. 8, Issue 1, 2019 · pp. 10–21 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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Performance of Equation-of-State for Hydrocarbon Dew Point Control in Gas Flow-line in a Nigerian Field
Abstract: Associated gas in a flow-line in a Nigerian field was suspected to be accountable for unaccounted-for gas in the flow-station. Gas molecular compositions of Low Pressure suction gas and Injection Discharge gas for operating conditions of pressure and temperature from the field were analysed by the use of Soave-Redlich Kwong and Peng-Robinson Equations of State with PVTp thermodynamic software. The phase envelope predicted the Hydrocarbon dew point(s) observable from the …
Published in Journal of Petroleum Engineering & Technology · Vol. 9, Issue 1, 2019 · pp. 7–13 Read article
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The Role Fixed Point Theorems in Differential Equations
Abstract: The purpose of this paper is to explore fixed point theorem from application point of view of differential equation and fractional differential equation. From previous 13 application were explained with various fixed point theorem applicable to differential equation. Theorems are like Banach fixed point theorem, Brouwer fixed point theorem, Borel fixed point theorem, Schauder fixed point theorem, Krasnoselskii’s fixed point theorem etc. It is observed that differential equation such as …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 8, Issue 2, 2021 · pp. 1–9 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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Lossy Image Compression Using Exponential Growth Equation and Encryption by Natural Exponential Function
Abstract: AbstractImage compression is an essential technology in transmission and storage of digital images because of vast data associated with them. So, image compression plays an important role in the transmission of digital images through the internet with less bandwidth and occupies less space in memory. This research suggests a new image compression method based on exponential growth equation. The exponential growth equation is used for the image compression. The effectiveness …
Published in Journal of Image Processing & Pattern Recognition Progress · Vol. 4, Issue 3, 2017 · pp. 46–55 Read article
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Computable Extension of New Advanced Fractional Kinetic Equation
Abstract: AbstractFirst, we obtain computable extensions of advanced fractional kinetic equation. The aim of this survey is to explore the behavior of physical and biological systems from the point of view of fractional calculus. Fractional calculus, integration and differentiation of an arbitrary or fractional order, provide new tools that expand the descriptive power of calculus beyond the familiar integer-order concepts of rates of change and area under a curve. Fractional calculus …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 4, Issue 2, 2017 · pp. 26–32 Read article
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BIS Processes in the Human Neural Networks and Asymptotic Periodic Solutions of the Evolution Equations in the Brain Nanosystem using Jacobi Elliptic Function
Abstract: Our perseverance is dependent upon the normal functioning and fluctuation of the brain. That functioning involves complex electrical activities. These in turn generate subtle waves which were first noticed and studied by Hans Berger. These are essentially electrical rhythms in the brain which, when recorded by means of instruments called electroencephalograms or EEG on a roll of paper, appear as complex wave forms. In this paper, based on Jacobi elliptic …
Published in Current Trends in Signal Processing · Vol. 3, Issue 3, 2013 · pp. 11–18 Read article
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Compare Newton-HSS Iteration Method and Picard-HSS Iteration Method for Solving the System of Weakly Nonlinear Equations
Abstract: So far several iterative methods have been proposed and used for solving the system of weakly nonlinear equations Ax = G(x). In this paper, we study the Newton-HSS iteration method and Picard-HSS iteration method for solve the system of weakly nonlinear equations. Then we compare these two methods. We discuss the performance of these methods, and numerical results. Cite this ArticleElham Farazande Shahraki. Compare Newton-HSS iteration method and Picard-HSS iteration …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 3, Issue 1, 2016 · pp. 1–6 Read article
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A STUDY: Validation of Creep Damage Constitutive Equations of Bar 257 Steels at 650°: A Study
Abstract: Validation of creep damage constitutive equations under the future loads, the left over lifetime is predicted to be quite limited. The main objective is to make prediction about the lifetime left because a growing stage of damage is encouraged by the previous history of loading. The ultimate goal is to render a loading spectrum that is complete in nature and predict about the time of keeping the material in the …
Published in Journal of Experimental & Applied Mechanics · Vol. 8, Issue 2, 2017 · pp. 39–44 Read article
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Non-linear Singular Integral Equations for Multiphase Flows in Petroleum Reservoir Engineering
Abstract: A very important problem of petroleum reservoir engineering is investigated by the present research. Consequently, an innovative and groundbreaking mathematical approach is introduced for the determination of the properties of the earth subsurface, when oil reserves together with water are moving through porous media. So, the multiphase flow problem of petroleum together with water is reduced to the solution of a non-linear singular integral equation, which is numerically solved by …
Published in Journal of Petroleum Engineering & Technology · Vol. 2, Issue 1-3, 2012 · pp. 73–82 Read article
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Preference assessment of energy and momentum equations over 2D-SKM method in compound channels
Abstract: Gradually varied flow in channels could be assessed and investigated from both the energy and momentum equations standpoints. Depending on what method is implemented, the computational results could be different. Currently, there is an ambiguity on the preference of utilizing the energy and momentum equations standpoints. This study attempts to respond to this ambiguity and the question that among these pair viewpoints which one would provide a closer solution to …
Published in Journal of Water Resource Engineering and Management · Vol. 6, Issue 1, 2019 · pp. 24–34 Read article
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Non-linear Integral Equations Ideal Solar Cells Analysis with One and Two Intermediate Bands
Abstract: An innovative and groundbreaking theory is proposed by using intermediate bands within the energy gap of the semiconductor in order to increase the efficiency of solar cells. Consequently, photons with energy less than the band gap may contribute to the output device by using the intermediate band or bands, in order to jump to the conduction band. This problem is reduced to the solution of non-linear integral equations and for …
Published in Journal of Alternate Energy Sources & Technologies · Vol. 4, Issue 2, 2013 · pp. 8–15 Read article
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Application of Homotopy Analysis Method and Adomian Decomposition Method for the Solution of Neutron Diffusion Equation in the Hemisphere and Cylindrical Reactors
Abstract: In the present paper, Homotopy Analysis Method and Adomian Decomposition Method are applied to obtain the analytical approximate solutions of neutron diffusion equation for both finite cylinders and bare hemisphere. Numerical results are provided by considering zero flux boundary (ZF) as well as extrapolated boundary conditions (EBCs). The explicit solution for critical radius and flux distributions are represented graphically. Keywords: Homotopy analysis method, Adomian decomposition method, ZF boundary conditions, neutron …
Published in Journal of Nuclear Engineering & Technology · Vol. 1, Issue 2-3, 2011 Read article
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Numerical Analysis of Oblique Impinge shock-wave/turbulent boundary-layer interaction Using Reynolds Average Navier Stroke Equations
Abstract: Interaction of shock waves with turbulent boundary layer plays an important role in the design and operability of high-speed aerospace vehicles and air-breathing engines. During interaction, the adverse pressure gradient of the shock is often strong enough to separate the boundary layer. Reynolds averaged Navier-Stokes simulations using conventional turbulence models do not predict the correct size and shape of the separation bubble in strong shock/turbulent boundary-layer interactions. The corresponding surface …
Published in Research & Reviews : Journal of Space Science & Technology · Vol. 8, Issue 3, 2019 · pp. 31–48 Read article