Efficient Solutions of Multidimensional Sixth-Order Boundary Value Problems Using Symmetric Generalized Jacobi-Galerkin Method by E. H. Doha, W. M. Abd-Elhameed

“…This paper presents some efficient spectral algorithms for solving linear sixth-order two-point boundary value problems in one dimension based on the application of the Galerkin method. The proposed algorithms are extended to solve the two-dimensional sixth-order differential equations. …”
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Affine Discontinuous Galerkin Method Approximation of Second-Order Linear Elliptic Equations in Divergence Form with Right-Hand Side in L1 by Abdeluaab Lidouh, Rachid Messaoudi

“…We consider the standard affine discontinuous Galerkin method approximation of the second-order linear elliptic equation in divergence form with coefficients in L∞Ω and the right-hand side belongs to L1Ω; we extend the results where the case of linear finite elements approximation is considered. …”
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Vibrations of Plates and Shells with Attached Mass by L. U. Sultanov, I. R. Garifullin

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Non-Linear Vibrations of Graphene Nanoplatelet-Reinforced Composite Beams using Non-Local Strain Gradient Theory by Ahmad Haghani

Subjects: “…galerkin method…”
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Implementing the Galerkin Method Associated with the Shifted Vieta-Lucas Polynomials for Studying Numerically the Bionanofluid Flow Which Is Saturated by Gyrotactic Microorganisms over a Slippery Stretching Sheet by M. M. Khader, M. M. Babatin, Ahmed M. Megahed, A. Eid

“…The suggested system will be converted to a computationally tractable form using the Galerkin method. The shifted Vieta-Lucas polynomials are then used as basis functions on the provided domain to solve the nonlinear system of ordinary differential equations that has been constructed (ODEs). …”
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Development of a high-order global dynamical core using the discontinuous Galerkin method for an atmospheric large-eddy simulation (LES) and proposal of test cases: SCALE-DG v0.8.0 by Y. Kawai, H. Tomita, H. Tomita

“…<p>Focusing on the future global atmospheric simulations with a grid spacing of O(10–100 m), we developed a global nonhydrostatic atmospheric dynamical core with high-order accuracy by applying a discontinuous Galerkin method (DGM) for horizontal and vertical discretization. …”
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A weak Galerkin finite element method for parabolic singularly perturbed convection-diffusion equations on layer-adapted meshes by Suayip Toprakseven, Seza Dinibutun

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Models, systems, networks in economics, engineering, nature and society by A.O. Lapich

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Global existence of weak solutions to a class of higher-order nonlinear evolution equations by Li-ming Xiao, Cao Luo, Jie Liu

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A New Wavelet Method for Solving a Class of Nonlinear Volterra-Fredholm Integral Equations by Xiaomin Wang

“…A new approach, Coiflet-type wavelet Galerkin method, is proposed for numerically solving the Volterra-Fredholm integral equations. …”
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Comparison of SUPG with Bubble Stabilization Parameters and the Standard SUPG by Xiaowei Liu, Jin Zhang

“…We study a streamline upwind Petrov-Galerkin method (SUPG) with bubble stabilization coefficients on quasiuniform triangular meshes. …”
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Wavelet-Galerkin Quasilinearization Method for Nonlinear Boundary Value Problems by Umer Saeed, Mujeeb ur Rehman

“…Quasilinearization technique is applied to linearize the nonlinear differential equation and then wavelet-Galerkin method is implemented to linearized differential equations. …”
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Numerical Solutions of Odd Order Linear and Nonlinear Initial Value Problems Using a Shifted Jacobi Spectral Approximations by A. H. Bhrawy, M. A. Alghamdi

“…A shifted Jacobi Galerkin method is introduced to get a direct solution technique for solving the third- and fifth-order differential equations with constant coefficients subject to initial conditions. …”
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Vortex-Induced Vibration of a Cable-Stayed Bridge by M. T. Song, D. Q. Cao, W. D. Zhu

“…Convergence of the dynamic response from Galerkin method is investigated. Numerical results show that the geometric nonlinearities of stay cables have significant influence on vortex-induced vibration of the cable-stayed bridge. …”
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A Numerical Algorithm for a Kirchhoff-Type Nonlinear Static Beam by Jemal Peradze

“…An approximate solution is found using the Galerkin method and the Jacobi nonlinear iteration process. …”
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On an initial-boundary value problem for the nonlinear Schrödinger equation by Herbert Gajewski

“…We prove a global existence and uniqueness theorem and establish a Galerkin method for solving numerically the problem.…”
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The Global Existence and Uniqueness of the Classical Solution with the Periodic Initial Value Problem for One-Dimension Klein-Gordon-Zakharov Equations by Cong Sun, Lixia Li

“…Through applying Galerkin method, we establish the approximating solution for one-dimension Klein-Gordon-Zakharov equations and obtain the local classical solution. …”
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On the Weak Solution to a Fractional Nonlinear Schrödinger Equation by Zujin Zhang, Xiaofeng Wang, Zheng-an Yao

“…We obtain the existence of a global weak solution to a fractional nonlinear Schrödinger equation by the Galerkin method. Its uniqueness is also discussed. In our proof, we use harmonic analysis techniques and compactness arguments.…”
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On a Fractional Nonlinear Hyperbolic Equation Arising from Relative Theory by Zujin Zhang, Xiaofeng Wang, Zheng-an Yao

“…We obtain the existence of a weak solution to a fractional nonlinear hyperbolic equation arising from relative theory by the Galerkin method. Its uniqueness is also discussed. Furthermore, we show the regularity of the obtained solution. …”
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Fluid-Induced Nonlinear Vibration of a Cantilevered Microtube with Symmetric Motion Constraints by Yong Guo

“…Based on the modified couple stress theory and the von Kármán relationship, the strain energy of the microtube can be deduced and then the governing equation of motion is derived by using the Hamilton principle. The Galerkin method is applied to produce a set of ordinary differential equations. …”
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