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8 results for “Laplace's Equation”
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Research ArticleOpen accessIn the keywordsPerturbation Iteration Transform Method for the Solution of Newell-Whitehead-Segel Model EquationsGrace O. Akinlabi, Sunday O. EdekiIn this study, a computational method referred to as Perturbation Iteration Transform Method (PITM), which is a combination of the conventional Laplace Transform Method (LTM) and the Perturbation Iteration Algorithm (PIA) is applied for the solution of Newell-Whitehead-Segel Equations (NWSEs). Three unique examples are considered and the results obtained are compared with their exact solutions graphically. Also, the results agree … …Journal of Mathematics and Statistics, Vol. 13, Issue 1 · 20 Feb 2017 · 6,987 accessesView PDFCite
Research ArticleOpen accessIn the keywordsOn the Variational Symmetries of P.D.E's Incorporating Boundary Value ConstraintsUchechukwu Michael Opara, Festus Irimisose Arunaye et al.A crucial interface between Optimization theory, Trace theory, and Lie Symmetry theory is brought to the fore in this paper, as an enhancement of standard known results established in Partial Differential Equation (P.D.E) analysis. In particular, the incorporation of compatible Boundary Value constraints in the re-assessment of admitted variational symmetries is a key process in the development of the discussions … …Journal of Mathematics and Statistics, Vol. 21, Issue 1 · 22 Jan 2025 · 8,433 accessesView PDFCite
Research ArticleOpen accessIn the keywordsThe Solution to Some Hypersingular Integral EquationsAlexander G. RammGel’fand, I. M., & Shilov, G. E. (1964). Generalized Functions. Volume I: Properties and Operations (1st ed., Vol. 1). Academic Press. Hörmander, L. (1998). The Analysis of Linear Partial Differential Operators I (1st ed.). Springer Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-96750-4 Ramm, A. G. (2022). The Navier-Stokes Problem (2nd ed.). Springer Nature. Ramm, A. G. (2023). Analysis of the Navier-Stokes problem (2nd ed.). … …Journal of Mathematics and Statistics, Vol. 20, Issue 1 · 25 May 2024 · 5,683 accessesView PDFCite
Research ArticleOpen accessIn the abstractExploring Mesh Generation and Quality Enhancement with Open Source CodesLeandro Alves Neves, José Márcio Machado, Julio Cesar Momente et al.The finite element method is a very reliable and precise technique for solving partial differential equations in three-dimensional domains, with relevant applications in several areas. However, 3D simulations by FEM require computer programs for solid modeling and automatic mesh generation and there are few examples of open source codes available and dedicated to these tasks. Unfortunately, these open source codes … …Journal of Computer Science, Vol. 14, Issue 7 · 19 Jul 2018 · 8,357 accessesView PDFCite
Research ArticleOpen accessIn the abstractSome Contributions to the Theory of Abstract Degenerate Volterra Integro-Differential EquationsMarko KostićIn this study, we contribute to the existing theory of abstract degenerate Volterra integro-differential equations in sequentially complete locally convex spaces. We investigate a class of abstract degenerate Volterra inclusions by using the multivalued linear operator approach, as well as a class of abstract degenerate multi-term fractional differential equations with Caputo derivatives by using the pure Laplace transform techniques. …Journal of Mathematics and Statistics, Vol. 12, Issue 2 · 17 Jun 2016 · 7,406 accessesView PDFCite
Research ArticleOpen accessIn the abstractNew Approach to Compute Integral TransformsA. Adawi, F. AwawdehIntegral transforms find special applicability within scientific and mathematical disciplines. A powerful and efficient homotopy methodology in evaluating integrals arises in integral transforms was presented. The method depends on solving a related first order linear differential equation by homotopy analysis method HAM. The Laplace transform, Fourier transform and the moment generating function of the standard normal distribution were used as … …Journal of Mathematics and Statistics, Vol. 4, Issue 2 · 30 Jun 2008 · 6,716 accessesView PDFCite
Research ArticleOpen accessIn the abstractThe Solution of Heat Conduction Equation with Mixed Boundary ConditionsNaser AbdelrazaqThe study is devoted to determine a solution for a non-stationary heat equation in axial symmetric cylindrical coordinates under mixed discontinuous boundary of the first and second kind conditions, with the aid of a Laplace transform and separation of variables method used to solve the considered problem which is the dual integral equations method. …Journal of Mathematics and Statistics, Vol. 2, Issue 1 · 31 Mar 2006 · 7,815 accessesView PDFCite
Research ArticleOpen accessAll words, across the recordOscillatory Behavior of Euler Cauchy Equation with Heaviside Step Function of a Bulge Function Over Various Time DomainJitendra Kumar Pati, Dillip Kumar Bhukta, Prashanta Kumar PandaIn this study authors discuss oscillatory property of Euler Cauchy Equation with heaviside step function of a bulge function in respect of homogenous and non homogenous output over different time intervals through general solution using Transform method. …Journal of Mathematics and Statistics, Vol. 17, Issue 1 · 7 Sep 2021 · 6,792 accessesView PDFCite