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A POD‐based–optimized finite difference CN‐extrapolated implicit scheme for the 2D viscoelastic wave equation †
Author(s) -
Xia Hong,
Luo Zhengdong
Publication year - 2017
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.4499
Subject(s) - mathematics , convergence (economics) , scheme (mathematics) , finite difference coefficient , stability (learning theory) , viscoelasticity , finite difference method , finite difference , finite difference scheme , wave equation , mathematical analysis , finite element method , mixed finite element method , physics , computer science , machine learning , economics , thermodynamics , economic growth
In this paper, we devote ourselves to establishing the unconditionally stable and absolutely convergent classical finite difference Crank‐Nicholson (CN) implicit (CFDCNI) scheme and optimized finite difference CN‐extrapolated implicit (OFDCNEI) scheme containing very few degrees of freedom but holding fully second‐order accuracy for the two‐dimensional viscoelastic wave via the proper orthogonal decomposition technique, analyzing the existence, stability, and convergence of the CFDCNI and OFDCNEI solutions, and using the numerical simulations to verify that the OFDCNEI scheme is far more superior than the CFDCNI scheme.