On preconditioned iterative methods for certain time-dependent partial differential equations

Zhong Zhi Bah*, Yu Mei Huang, Kwok Po NG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)

Abstract

When the Newton method or the fixed-poin t method is employed to solve the systems of nonlinear equations arising in the sinc-Galerkin discretization of certain time-dependent partial differential equations, in each iteration step we need to solve a structured subsystem of linear equations iteratively by, for example, a Krylov subspace method such as the preconditioned GMRES. In this paper, based on the tensor and the Toeplitz structures of the linear subsystems we construct structured preconditioners for their coefficient matrices and estimate the eigenvalue bounds of the preconditioned matrices under certain assumptions. Numerical examples are given to illustrate the effectiveness of the proposed preconditioning methods. It has been shown that a combination of the Newton/fixed-point iteration with the preconditioned GMRES method is efficient and robust for solving the systems of nonlinear equations arising from the sinc-Galerkin discretization of the time-dependent partial differential equations.

Original languageEnglish
Pages (from-to)1019-1037
Number of pages19
JournalSIAM Journal on Numerical Analysis
Volume47
Issue number2
DOIs
Publication statusPublished - 2009

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Eigenvalue bound
  • GMRES method
  • Preconditioning
  • Sinc-Galerkin discretization
  • Time-dependent partial differential equation
  • Toeplitzlike matrix

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