A parallel preconditioning technique for boundary value methods

DOI10.1016/0168-9274(93)90002-9zbMath0805.65077OpenAlexW1975982894MaRDI QIDQ1315826

Donato Trigiante, Luigi Brugnano

Publication date: 2 February 1995

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(93)90002-9

zbMATH Keywords

convergencepreconditioningparallel computationinitial value problemboundary value methodtwo-step difference schemestepsize selectionlarge scale test problems

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical computation of matrix norms, conditioning, scaling (65F35) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite difference and finite volume methods for ordinary differential equations (65L12) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items

The role of difference equations in numerical analysis ⋮ Variable-step boundary value methods based on reverse Adams schemes and their grid redistribution ⋮ Boundary value methods based on Adams-type methods ⋮ High-order multistep methods for boundary value problems ⋮ Parallel block preconditioning for the solution of boundary value methods ⋮ Parallel iterative solvers for boundary value methods ⋮ Dahlquist's barriers and much beyond ⋮ Boundary value methods for transient solutions of queueing networks with variant vacation policy ⋮ A boundary value approach to the numerical solution of initial value problems by multistep methos^† ⋮ Parallel implementation of block boundary value methods for ODEs ⋮ 50 Years of Time Parallel Time Integration ⋮ Preconditioned iterative method for boundary value method discretizations of a parabolic optimal control problem ⋮ A parallel preconditioning technique for boundary value methods ⋮ Stability properties of some boundary value methods

Uses Software

• ODEPACK

Cites Work

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• A parallel direct method for solving initial value problems for ordinary differential equations
• Parallel implementation of BVM methods
• Boundary value methods and BV-stability in the solution of initial value problems
• Inertia characteristics of self-adjoint matrix polynomials
• Theory of difference equations: Numerical methods and applications
• The convergence of the method of conjugate gradients at isolated extreme points of the spectrum
• Stability of some boundary value methods for the solution of initial value problems
• A parallel preconditioning technique for boundary value methods
• Stability properties of some boundary value methods
• Two-step boundary value methods in the solution of ODEs
• Boundary value techniques for initial value problems in ordinary differential equations
• Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
• The Lanczos Biorthogonalization Algorithm and Other Oblique Projection Methods for Solving Large Unsymmetric Systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Reduction to Tridiagonal Form and Minimal Realizations
• Reduction of a General Matrix to Tridiagonal Form