Results 11 to 20 of about 101,709 (214)
Axioms, 2022 This paper is concerned with numerical solutions to Volterra integro-differential equations with weakly singular kernels. Making use of the transformed fractional Jacobi polynomials, we develop a class of piecewise fractional Galerkin methods for solving
Haiyang Li, Junjie Ma
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Galerkin eigenvector approximations [PDF]
Mathematics of Computation, 2000 39 ...
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Uncertainty Analysis of Neutron Diffusion Eigenvalue Problem Based on Reduced-order Model
Yuanzineng kexue jishu, 2023 In order to improve the efficiency of core physical uncertainty analysis based on sampling statistics, the proper orthogonal decomposition (POD) and Galerkin projection method were combined to study the application feasibility of reduced-order model ...
In order to improve the efficiency of core physical uncertainty analysis based on sampling statistics, the proper orthogonal decomposition (POD) and Galerkin projection method were combined to study the application feasibility of reduced-order model based on POD-Galerkin method in core physical uncertainty analysis. The two-dimensional two group TWIGL benchmark question was taken as the research object, the key variation characteristics of the core flux distribution were extracted under the finite perturbation of the group constants of each material region, and the full-order neutron diffusion problem was projected on the variation characteristics to establish a reduced-order neutron diffusion model. The reduced-order model was used to replace the full-order model to carry out the uncertainty analysis of the group constants of the material region. The results show that the bias of the mathematical expectation of keff calculated by reduced-order and full-order models is close to 1 pcm. In addition, compared with the calculation time required for uncertainty analysis of full-order model, the analysis time of reduced-order model (including the calculation time of the full-order model required for the construction of reduced-order model) is only 11.48%, which greatly improves the efficiency of uncertainty analysis. The biases of mathematical expectation of keff calculated by reduced-order and full-order models based on Latin hypercube sampling and simple random sampling are less than 8 pcm, and under the same sample size, the bias from the Latin hypercube sampling result is smaller. From the TWIGL benchmark test results, under the same sample size, Latin hypercube sampling method is more recommended for POD-Galerkin reduced-order model.
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EXPLORING TRANSIENT, NEUTRONIC, REDUCED-ORDER MODELS USING DMD/POD-GALERKIN AND DATA-DRIVEN DMD [PDF]
EPJ Web of Conferences, 2021 There is growing interest in the development of transient, multiphysics models for nuclear reactors and analysis of uncertainties in those models. Reduced-order models (ROMs) provide a computationally cheaper alternative to compute uncertainties. However,
Elzohery Rabab, Roberts Jeremy
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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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Numerical Quantum Field Theory on the Continuum and a New Look at Perturbation Theory [PDF]
, 2001 The Source Galerkin method finds approximate solutions to the functional differential equations of field theories in the presence of external sources. While developing this process, it was recognized that approximations of the spectral representations of
D. Petrov +12 more
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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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Stability under Galerkin truncation of A-stable Runge--Kutta discretizations in time [PDF]
, 2014 We consider semilinear evolution equations for which the linear part is normal and generates a strongly continuous semigroup and the nonlinear part is sufficiently smooth on a scale of Hilbert spaces.
Oliver, Marcel, Wulff, Claudia
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Optimality Properties of Galerkin and Petrov–Galerkin Methods for Linear Matrix Equations [PDF]
Vietnam Journal of Mathematics, 2020 Galerkin and Petrov-Galerkin methods are some of the most successful solution procedures in numerical analysis. Their popularity is mainly due to the optimality properties of their approximate solution. We show that these features carry over to the (Petrov-)Galerkin methods applied for the solution of linear matrix equations.
Palitta D., Simoncini V.
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Advances in Mechanical Engineering, 2019 In this work, we deal with high-order solver for incompressible flow based on velocity correction scheme with discontinuous Galerkin discretized velocity and standard continuous approximated pressure.
Liyang Xu +5 more
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