Results 31 to 40 of about 117 (97)
Analysis of Spectral Tau Method for Approximate Solution of Fourth‐Order BVP in Hilbert Spaces
Journal of Mathematics, Volume 2026, Issue 1, 2026.This research explores the effectiveness of the spectral Tau method for solving fourth‐order differential boundary value problem (FBVP). We transform this FBVP into a Volterra–Fredholm integral equation (VFIE). By applying Banach’s fixed‐point theorem, we investigate the existence and uniqueness of the solution for the VFIE form of the FBVP equation ...
Javad Shokri, Smritijit Sen
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Sinc-Galerkin method and a higher-order method for a 1D and 2D time-fractional diffusion equations
Boundary Value ProblemsIn this article, a new numerical algorithm for solving a 1-dimensional (1D) and 2-dimensional (2D) time-fractional diffusion equation is proposed. The Sinc-Galerkin scheme is considered for spatial discretization, and a higher-order finite difference ...
Man Luo, Da Xu, Xianmin Pan
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Journal of Mathematics, Volume 2026, Issue 1, 2026.In this study, we first model the space‐fractional advection equation by choosing an exact solution under certain restrictions. Then, the forcing term is determined according to that solution. Secondly, we present a numerical solution for a class of space‐fractional advection‐diffusion equations with a nonlinear source term involving both time and ...
Muhammad Hakim Ali Qasmi +4 more
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Symmetrization of the sinc-Galerkin method for boundary value problems [PDF]
Mathematics of Computation, 1986 The Sinc-Galerkin method developed in [5], when applied to the second-order selfadjoint boundary value problem, gives rise to a nonsymmetric coefficient matrix. The technique in [5] is based on weighting the Galerkin inner products in such a way that the method will handle boundary value problems with regular singular points.
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Analyze Second‐Order PDEs Using the Volterra–Fredholm Integral Equation
Journal of Function Spaces, Volume 2025, Issue 1, 2025.In this study, we propose a novel approach to address a particular second‐order partial differential equation along with its boundary value conditions (SPDEs). In this process, we transfer the SPDEs problem into Volterra–Fredholm integral equation (VFIE), and we perform the Tau method bases on orthogonal Legendre polynomials directly, for solution of ...
Choonkil Park +2 more
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ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 104, Issue 9, September 2024.Abstract In this paper, we focus on scattering of non‐periodic incident fields in three‐dimensional bi‐periodic structures, as they can not be solved by the classical methods used for the quasi‐periodic scattering problems. To solve such non‐periodic scattering problems, the Floquet–Bloch transform, which decomposes the unbounded problem into a family ...
Tilo Arens +2 more
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Application of Sinc-Galerkin Method for Solving Space-Fractional Boundary Value Problems [PDF]
Mathematical Problems in Engineering, 2015 We employ the sinc-Galerkin method to obtain approximate solutions of space-fractional order partial differential equations (FPDEs) with variable coefficients. The fractional derivatives are used in the Caputo sense. The method is applied to three different problems and the obtained solutions are compared with the exact solutions of the problems. These
Sertan Alkan, Aydin Secer
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Sinc-Galerkin Method For The Solution Of Problems In Calculus Of Variations
, 2011 {"references": ["L. Elsgolts, Differential Equations and Calculus of Variations, Mir,\nMoscow, 1977 (translated from the Russian by G. Yankovsky).", "I.M. Gelfand, S.V. Fomin, Calculus of Variations, Prentice-Hall,\nEnglewood Cliffs, NJ, 1963.", "C.F. Chen, C.H. Hsiao, A walsh series direct method for solving\nvariational problems, J. Franklin Inst.vol.
M. Zarebnia, N. Aliniya
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Solving the first Painleve equation using the Sinc-Galerkin method
International Journal of Applied Mathematical Research, 2012 The main goal of this paper is to solve the ?rst Painleve equation using the sinc-Galerkin method. In order to obtain this goal, we ?rst describe brie?y the sinc-Gelrkin method, and then we apply it to the ?rst Painleve equation. At last, the numerical result is shown to demonstrate the power and accuracy of the method.
Ali Salimi shamloo +2 more
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Acoustic Green's Functions using the 2D Sinc-Galerkin Method
, 2014 In many acoustic problems, the radiated sound field is dominated by scattering effects. Green's functions represent the scattering behaviour of a particular geometry and are required to propagate acoustic disturbances through complex geometries using integral methods.
Harwood, Adrian R.G. +1 more
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