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The Galerkin Method for Solving Strongly Nonlinear Oscillators [PDF]
The Scientific World Journal, 2022 In this paper, we make use of the Galerkin method for solving nonlinear second-order ODEs that are related to some strongly nonlinear oscillators arising in physics and engineering. We derive the iterative schemes for finding the coefficients that appear
Alvaro H. S. Salas
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Galerkin-finite difference method for fractional parabolic partial differential equations [PDF]
MethodsXThe fractional form of the classical diffusion equation embodies the super-diffusive and sub-diffusive characteristics of any flow, depending on the fractional order. This study aims to approximate the solution of parabolic partial differential equations
Md. Shorif Hossan +2 more
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The Dual Characteristic-Galerkin Method
Comptes Rendus. MathématiqueThe Dual Characteristic-Galerkin method (DCGM) is conservative, precise and experimentally positive. We present the method and prove convergence and $L^2$-stability in the case of Neumann boundary conditions. In a 2D numerical finite element setting (FEM)
Hecht, Frédéric, Pironneau, Olivier
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Journal of Modern Power Systems and Clean Energy, 2021 In power systems, there are many uncertainty factors such as power outputs of distributed generations and fluctuations of loads. It is very beneficial to power system analysis to acquire an explicit function describing the relationship between these ...
Hao Wu +5 more
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Journal of Harbin University of Science and Technology, 2022 The equivalence between direct flux reconstruction method and discontinuous Galerkin method for solving parabolic equation and convection-diffusion equation is studied.
BI Hui, LIU Lei
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A stabilizer free weak Galerkin method for the Biharmonic Equation on Polytopal Meshes [PDF]
SIAM Journal on Numerical Analysis, 2019 A new stabilizer free weak Galerkin (WG) method is introduced and analyzed for the biharmonic equation. Stabilizing/penalty terms are often necessary in the finite element formulations with discontinuous approximations to ensure the stability of the ...
X. Ye, Shangyou Zhang
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Buildings, 2023 A common strategy for studying the nonlinear vibrations of beams is to discretize the nonlinear partial differential equation into a nonlinear ordinary differential equation or equations through the Galerkin method.
Yunbo Zhang, Kun Huang, Wei Xu
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Communications in Mathematical Research, 2020 Recent years have witnessed growing interests in solving partial differential equations by deep neural networks, especially in the high-dimensional case.
Jingrun Chen, Rui Du, Keke Wu
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Numerical Solution of Non-Linear Prey-Predator System using Finite Elements Method [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2007 A non-linear prey-predator system solved numerically by Galerkin method, and we compare these results with the results of Pius Peter Nyaanga[6] who used finite difference methods, we found that Galerkin finite elements method is faster than finite ...
Saad Manaa, Ahmed Qasem
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A superconvergent hybridisable discontinuous Galerkin method for linear elasticity [PDF]
International Journal for Numerical Methods in Engineering, 2018 The first superconvergent hybridisable discontinuous Galerkin method for linear elastic problems capable of using the same degree of approximation for both the primal and mixed variables is presented.
R. Sevilla +3 more
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