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Approximate inversion method for time‐fractional subdiffusion equations
Author(s) -
Lu Xin,
Pang HongKui,
Sun HaiWei,
Vong SeakWeng
Publication year - 2018
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2132
Subject(s) - toeplitz matrix , mathematics , triangular matrix , inversion (geology) , finite difference , block (permutation group theory) , finite difference method , coefficient matrix , mathematical analysis , geometry , pure mathematics , paleontology , eigenvalues and eigenvectors , physics , structural basin , quantum mechanics , invertible matrix , biology
Summary The finite‐difference method applied to the time‐fractional subdiffusion equation usually leads to a large‐scale linear system with a block lower triangular Toeplitz coefficient matrix. The approximate inversion method is employed to solve this system. A sufficient condition is proved to guarantee the high accuracy of the approximate inversion method for solving the block lower triangular Toeplitz systems, which are easy to verify in practice and have a wide range of applications. The applications of this sufficient condition to several existing finite‐difference schemes are investigated. Numerical experiments are presented to verify the validity of theoretical results.