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pro vyhledávání: '"Wu, Boying"'
In this paper, we concentrate on the superconvergence of the local discontinuous Galerkin method with generalized numerical fluxes for one-dimensional linear time-dependent fourth-order equations. The adjustable numerical viscosity of the generalized
Externí odkaz:
http://arxiv.org/abs/2409.14004
This paper deals with a novel nonlinear coupled nonlocal reaction-diffusion system proposed for image restoration, characterized by the advantages of preserving low gray level features and textures.The gray level indicator in the proposed model is re
Externí odkaz:
http://arxiv.org/abs/2407.04347
In this paper, we study a class of fractional $1$-Laplacian diffusion equations with variable orders, proposed as a model for multiplicative noise removal. The existence and uniqueness of the weak solution are proven. To overcome the difficulties in
Externí odkaz:
http://arxiv.org/abs/2311.11680
Physics-informed neural networks have shown great promise in solving partial differential equations. However, due to insufficient robustness, vanilla PINNs often face challenges when solving complex PDEs, especially those involving multi-scale behavi
Externí odkaz:
http://arxiv.org/abs/2310.11789
In this paper, we present optimal error estimates of the local discontinuous Galerkin method with generalized numerical fluxes for one-dimensional nonlinear convection-diffusion systems. The upwind-biased flux with adjustable numerical viscosity for
Externí odkaz:
http://arxiv.org/abs/2209.03604
Publikováno v:
In Applied Mathematical Modelling October 2024 134:500-519
We present a new fractional Taylor formula for singular functions whose Caputo fractional derivatives are of bounded variation. It bridges and ``interpolates" the usual Taylor formulas with two consecutive integer orders. This enables us to obtain an
Externí odkaz:
http://arxiv.org/abs/2006.00667
This paper investigates superconvergence properties of the local discontinuous Galerkin methods with generalized alternating fluxes for one-dimensional linear convection-diffusion equations. By the technique of constructing some special correction fu
Externí odkaz:
http://arxiv.org/abs/1912.08732
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Publikováno v:
In Applied Mathematics Letters November 2023 145