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Analysis of the L1 scheme for a time fractional parabolic–elliptic problem involving weak singularity
Author(s) -
Santra Sudarshan,
Mohapatra Jugal
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.6850
Subject(s) - mathematics , mathematical analysis , discretization , singularity , domain (mathematical analysis) , convergence (economics) , elliptic operator , parabolic partial differential equation , boundary value problem , elliptic curve , partial differential equation , economics , economic growth
A time fractional initial boundary value problem of mixed parabolic–elliptic type is considered. The domain of such problem is divided into two subdomains. A reaction–diffusion parabolic problem is considered on the first domain, and on the second, a convection–diffusion elliptic type problem is considered. Such problem has a mild singularity at the initial time t = 0 . The classical L1 scheme is introduced to approximate the temporal derivative, and a second order standard finite difference scheme is used to approximate the spatial derivatives. The domain is discretized with uniform mesh for both directions. It is shown that the order of convergence is more higher away from t = 0 than the order of convergence on the whole domain. To show the efficiency of the scheme, numerical results are provided.