A POD‐based–optimized finite difference CN‐extrapolated implicit scheme for the 2D viscoelastic wave equation† |
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| Authors: | Hong Xia Zhengdong Luo |
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| Institution: | 1. School of Control and Computer Engineering, North China Electric Power University, Beijing, China;2. School of Mathematics and Physics, North China Electric Power University, Beijing, China |
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| Abstract: | 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. |
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| Keywords: | classical finite difference Crank‐Nicholson implicit scheme existence stability and convergence numerical simulation optimized finite difference Crank‐Nicholson extrapolated implicit scheme |
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