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Local discontinuous Galerkin approximations to fractional Bagley‐Torvik equation
Author(s) -
Izadi Mohammad,
Negar Mohammad Reza
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6233
Subject(s) - mathematics , discretization , discontinuous galerkin method , boundary value problem , variable (mathematics) , galerkin method , finite element method , approximations of π , mathematical analysis , physics , thermodynamics
In this research, numerical approximation to fractional Bagley‐Torvik equation as an important model arising in fluid mechanics is investigated. Our discretization algorithm is based on the local discontinuous Galerkin (LDG) schemes along with using the natural upwind fluxes, which enables us to solve the model problem element by element. This means that we require to solve a low‐order system of equations in each subinterval, hence avoiding the need for a full global solution. The proposed schemes are tested on a range of initial‐ and boundary‐value problems including a variable coefficient example, a nonsmooth problem, and some oscillatory test cases with exact solutions. Also, the validation of the proposed methods was compared with those obtained available existing computational procedures. Overall, it was found that LDG methods indicated highly satisfactory performance with comparatively lower degree of polynomials and number of elements compared with other numerical models.