Circulant-block preconditioners for solving ordinary differential equations
Applied Mathematics and Computation
Skew-Circulant Preconditioners for Systems of LMF-Based ODE Codes
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Strang-Type Preconditioners for Differential-Algebraic Equations
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Circulant preconditioned WR-BVM methods for ODE systems
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Preconditioned WR-LMF-based method for ODE systems
Journal of Computational and Applied Mathematics
Block preconditioners with circulant blocks for general linear systems
Computers & Mathematics with Applications
BCCB preconditioners for solving linear systems from delay differential equations
Computers & Mathematics with Applications
Boundary value methods for transient solutions of queueing networks with variant vacation policy
Journal of Computational and Applied Mathematics
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In this paper, a recently introduced block circulant preconditioner for the linear systems of the codes for ordinary differential equations (ODEs) is investigated. Most ODE codes based on implicit formulas, at each integration step, need the solution of one or more unsymmetric linear systems that are often large and sparse. Here, the boundary value methods, a class of implicit methods for the numerical integration of ODEs based on linear multistep formulas, are considered more in detail for initial value problems.Theoretical and practical arguments are given to show that the block circulant preconditioner can give fast preconditioned iterations for various classes of differential problems. Moreover, the P-circulants, a recently introduced circulant approximation for unsymmetric Toeplitz matrices, are shown to be more suitable sometimes than other circulant matrices for the underlying block preconditioner.