A review: Applications of the spectral finite element method
MB Hafeez, M Krawczuk - Archives of Computational Methods in …, 2023 - Springer
Abstract The Spectral Finite Element Technique (SFEM) has Several Applications in the
Sciences, Engineering, and Mathematics, which will be Covered in this Review Article. The …
Sciences, Engineering, and Mathematics, which will be Covered in this Review Article. The …
Numerical methods for nonlocal and fractional models
Partial differential equations (PDEs) are used with huge success to model phenomena
across all scientific and engineering disciplines. However, across an equally wide swath …
across all scientific and engineering disciplines. However, across an equally wide swath …
A spectrally accurate approximation to subdiffusion equations using the log orthogonal functions
In this paper, we develop and analyze a spectral-Galerkin method for solving subdiffusion
equations, which contain Caputo fractional derivatives with order ν∈(0,1). The basis …
equations, which contain Caputo fractional derivatives with order ν∈(0,1). The basis …
Multi-domain spectral collocation method for variable-order nonlinear fractional differential equations
T Zhao, Z Mao, GE Karniadakis - Computer Methods in Applied Mechanics …, 2019 - Elsevier
Spectral and spectral element methods using Galerkin type formulations are efficient for
solving linear fractional PDEs (FPDEs) of constant order but are not efficient in solving …
solving linear fractional PDEs (FPDEs) of constant order but are not efficient in solving …
Fractional wave models and their experimental applications
BA Malomed - Fractional Dispersive Models and Applications: Recent …, 2024 - Springer
A focused summary of one-and two-dimensional models for linear and nonlinear wave
propagation in fractional media is given. The basic models, which represent fractional …
propagation in fractional media is given. The basic models, which represent fractional …
Optimal Petrov–Galerkin spectral approximation method for the fractional diffusion, advection, reaction equation on a bounded interval
In this paper we investigate the numerical approximation of the fractional diffusion,
advection, reaction equation on a bounded interval. Recently the explicit form of the solution …
advection, reaction equation on a bounded interval. Recently the explicit form of the solution …
A robust higher-order finite difference technique for a time-fractional singularly perturbed problem
A higher-order finite difference method is developed to solve the variable coefficients
convection–diffusion singularly perturbed problems (SPPs) involving fractional-order time …
convection–diffusion singularly perturbed problems (SPPs) involving fractional-order time …
Finite difference/spectral element method for one and two-dimensional Riesz space fractional advection–dispersion equations
M Saffarian, A Mohebbi - Mathematics and Computers in Simulation, 2022 - Elsevier
In this paper, we propose an efficient numerical method for the solution of one and two
dimensional Riesz space fractional advection–dispersion equation. To this end, we use the …
dimensional Riesz space fractional advection–dispersion equation. To this end, we use the …
An h-p version of the continuous Petrov-Galerkin finite element method for Riemann-Liouville fractional differential equation with novel test basis functions
W Bu, A Xiao - Numerical Algorithms, 2019 - Springer
In this paper, we develop an hp version of finite element method for one-dimensional
fractional differential equation− 0 D x α u+ Au= f (x) -_0D_x^αu+Au=f(x) with Dirichlet …
fractional differential equation− 0 D x α u+ Au= f (x) -_0D_x^αu+Au=f(x) with Dirichlet …
A unified Petrov–Galerkin spectral method and fast solver for distributed-order partial differential equations
Fractional calculus and fractional-order modeling provide effective tools for modeling and
simulation of anomalous diffusion with power-law scalings. In complex multi-fractal …
simulation of anomalous diffusion with power-law scalings. In complex multi-fractal …