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50 results for “Series Solution”
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Research ArticleOpen accessPhrase in the titleApproximate Series Solution of Nonlinear, Fractional Klein-Gordon Equations Using Fractional Reduced Differential Transform MethodEman Abuteen, Asad Freihat, Mohammed Al-Smadi et al.This analysis proposes an analytical-numerical approach for providing solutions of a class of nonlinear fractional Klein-Gordon equation subjected to appropriate initial conditions in Caputo sense by using the Fractional Reduced Differential Transform Method (FRDTM). This technique provides the solutions very accurately and efficiently in convergent series formula with easily computable coefficients. The behavior of the approximate series solution for different … …Journal of Mathematics and Statistics, Vol. 12, Issue 1 · 26 Mar 2016 · 7,901 accessesView PDFCite
Research ArticleOpen accessPhrase in the titlePower Series Solution for a Two-step Reactive-diffusive Equation with Variable Pre-exponential FactorE.A. Adebile, O.K. Koriko, U.S. IdiongWe discussed in this research a power series method for solution of a two-step reactive-diffusive equation with variable pre-exponential factor. A transformation was used to fit in the geometry of the model to allow an asymptotic series expansion which is invoked in a two compartmental regions with respect to the spatial variable. Adequate matching conditions were used at the interface … …Journal of Mathematics and Statistics, Vol. 4, Issue 2 · 30 Jun 2008 · 6,851 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleAnalytical Solution Based on a New Series along with the Numeric Solution of the Non-Homogeneous Transient Heat Conduction Equation, in Hollow Cylinder under General Mixed Boundary ConditionsMehdi Zare, F. KardanIn this study, the problem of transient conduction heat transfer for an infinite hollow cylinder under non-homogeneous mixed boundary conditions at the both surfaces simultaneously in radial direction with general heat source depend on time and radius, also general initial condition by the method of superposition and separation variables, is solved and temperature distribution is obtained analytically. A new series … …American Journal of Engineering and Applied Sciences, Vol. 11, Issue 2 · 20 Apr 2018 · 9,486 accessesView PDFCite
Research ArticleOpen accessEvery word in the titleAnalytical Solution of Temperature Field in Hollow Cylinder under Time Dependent Boundary Condition Using Fourier seriesGolamali atefi, Mohammad Ali Abdous, Abdolsaeid GanjehkaviriThe objective of this study is to derive an analytical solution of one dimensional heat conduction equation applied in a hollow cylinder, which is subjected to a periodic boundary condition at the outer surface while the inner surface is insulated. The material is assumed to be homogenous and isotropic with time-independent thermal properties. Because of the time-dependent term in the … …American Journal of Engineering and Applied Sciences, Vol. 1, Issue 2 · 30 Jun 2008 · 7,533 accessesView PDFCite
Research ArticleOpen accessIn the keywordsAn Expansion Iterative Technique for Handling Fractional Differential Equations Using Fractional Power Series SchemeRadwan Abu-Gdairi, Mohammed Al-Smadi, Ghaleb GumahIn this study, we present a new analytical numerical technique for solving a class of time Fractional Differential Equations (FDEs) with variable coefficients based on the generalized Taylor series formula in the Caputo sense. This method provided the solution in the form of a rapidly convergent power series under a multiple fractional differentiability with easily computable components. An efficacious experiment … …Journal of Mathematics and Statistics, Vol. 11, Issue 2 · 18 Sep 2015 · 7,807 accessesView PDFCite
Research ArticleOpen accessIn the abstractSmart Weather Data Management System for Sustainable Agriculture in Maharashtra Using Machine LearningAishwarya V. Kadu, Kuraparthi Tirumala V. ReddyAgriculture will benefit greatly from efficient weather data sustainable management. Data can be utilized to schedule the prediction yield, crop growth, and irrigation. This paper collects real-time meteorological station data via APIs, primarily focusing on the weather data sustainable management system and data related to Maharashtra Wardha, India, which is involved in a live series period. Agriculture can make potential … …Journal of Computer Science, Vol. 21, Issue 7 · 7 Jul 2025 · 3,507 accessesView PDFCite
Research ArticleOpen accessIn the abstractBlockchain: An Efficient Intelligent Agreement for Patents and TrademarksVikram Shirol, Shanmuga RathinamIntellectual property security faces problems in the digital era, with growing piracy, AI-generated works, and global compliance problems, Creations, designs, trademarks, and trade secrets are all protected by Intellectual Property (IP) rights; yet, there are several issues with IP rights management and enforcement around the world. The benefits of blockchain technology include decentralization, transparency, and immutability. Therefore, blockchain offers to … …Journal of Computer Science, Vol. 21, Issue 3 · 20 Feb 2025 · 5,491 accessesView PDFCite
Research ArticleOpen accessIn the abstractFree Vibration Analysis of Rectangular Cantilever Plates Using the Hyperbolic-Trigonometric SeriesMikhail V. Sukhoterin, Sergey O. Baryshnikov, Dmitry A. AksenovThe purpose of this paper is to develop a numerical analytical method for an accurate solution to the problem on frequencies and mode shapes of a rectangular cantilever plate. The problem is reduced to an infinite system of linear algebraic equations relative to ratios of trigonometric series, which contains vibration frequency as a parameter. The core of the method is … …American Journal of Applied Sciences, Vol. 13, Issue 12 · 23 Dec 2016 · 7,283 accessesView PDFCite
Research ArticleOpen accessIn the abstractFitted Reproducing Kernel Method for Solving a Class of Third-Order Periodic Boundary Value ProblemsAsad Freihat, Radwan Abu-Gdairi, Hammad Khalil et al.In this article, the reproducing kernel Hilbert space W24 [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast accurately and efficiently series solutions with easily computable coefficients throughout evolution the algorithm under constraint periodic conditions within required grid points. The … …American Journal of Applied Sciences, Vol. 13, Issue 5 · 11 May 2016 · 7,647 accessesView PDFCite
Research ArticleOpen accessIn the abstractNew Hybrid Block Method with Three Off-Step Points for Solving First Order Ordinary Differential EquationsRa’ft Abdelrahim, Zurni Omar, John Olusola KuboyeA new single-step hybrid block method with three off-step points for the solution of first order ordinary differential equations is proposed. The strategy employed to develop this method is interpolating the power series approximate solution at xn and off-step points and collocating the derivative of the power at xn+1. The class of linear multistep method derived is then simultaneously applied … …American Journal of Applied Sciences, Vol. 13, Issue 2 · 18 Feb 2016 · 8,234 accessesView PDFCite