TY - JOUR
T1 - Numerical solution of the boundary value problems for the biharmonic equations via quasiseparable representations
AU - Ben-Artzi, M.
AU - Eidelman, Y.
AU - Fishelov, D.
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2025/2
Y1 - 2025/2
N2 - The paper incorporates new methods of numerical linear algebra for the approximation of the biharmonic equation with potential, namely, numerical solution of the Dirichlet problem for (Formula presented.) High-order discrete finite difference operators are presented, constructed on the basis of discrete Hermitian derivatives, and the associated Discrete Biharmonic Operator (DBO). It is shown that the matrices associated with the discrete operator belong to a class of quasiseparable matrices of low rank matrices. The application of quasiseparable representation of rank structured matrices yields fast and stable algorithm for variable potentials c(x). Numerical examples corroborate the claim of high order accuracy of the algorithm, with optimal complexity O(N).
AB - The paper incorporates new methods of numerical linear algebra for the approximation of the biharmonic equation with potential, namely, numerical solution of the Dirichlet problem for (Formula presented.) High-order discrete finite difference operators are presented, constructed on the basis of discrete Hermitian derivatives, and the associated Discrete Biharmonic Operator (DBO). It is shown that the matrices associated with the discrete operator belong to a class of quasiseparable matrices of low rank matrices. The application of quasiseparable representation of rank structured matrices yields fast and stable algorithm for variable potentials c(x). Numerical examples corroborate the claim of high order accuracy of the algorithm, with optimal complexity O(N).
KW - Biharmonic equations
KW - Dirichlet problem
KW - Hermitian derivative
KW - High-order difference scheme
KW - Numerical solution
KW - Potential
KW - Quassiseparable representation of matrices
UR - http://www.scopus.com/inward/record.url?scp=85188930610&partnerID=8YFLogxK
U2 - 10.1007/s11075-024-01809-9
DO - 10.1007/s11075-024-01809-9
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AN - SCOPUS:85188930610
SN - 1017-1398
VL - 98
SP - 625
EP - 649
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 2
ER -