Almost block diagonal linear systems: sequential and parallel solution techniques, and applications
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Publication:4814485
DOI<275::AID-NLA198>3.0.CO;2-G 10.1002/1099-1506(200007/08)7:5<275::AID-NLA198>3.0.CO;2-GzbMath1051.65018OpenAlexW2078003747MaRDI QIDQ4814485
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Publication date: 7 September 2004
Full work available at URL: https://doi.org/10.1002/1099-1506(200007/08)7:5<275::aid-nla198>3.0.co;2-g
numerical examplesboundary value problemsiterative algorithmscollocation methodsfinite differencesparallel computingsurvey paperalmost block diagonal systemsdirect algorithmsmultiple shooting methods
Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Iterative numerical methods for linear systems (65F10) Parallel numerical computation (65Y05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05) Direct numerical methods for linear systems and matrix inversion (65F05) Finite difference and finite volume methods for ordinary differential equations (65L12)
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Uses Software
Cites Work
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- Vector- and parallelisation of ODE BVP codes
- Parallel solution of almost block diagonal systems on the CRAY Y-MP using level 3 BLAS
- Parallel treatment of block-bidiagonal matrices in the solution of ordinary differential boundary value problems
- On parallel methods for boundary value ODEs
- Solving almost block diagonal systems on parallel computers
- Codes for almost block diagonal systems
- On efficient direct methods for conforming spectral domain decomposition techniques
- Efficient classes of Runge-Kutta methods for two-point boundary value problems
- A fast algorithm for solving the tensor product collocation equations
- Second-order splitting combined with orthogonal cubic spline collocation method for the Kuramoto-Sivashinsky equation
- High order methods for the numerical solution of two-point boundary value problems
- An alternating direction implicit method for orthogonal spline collocation linear systems
- The numerical solution of laminar flow in a re-entrant tube geometry by a Chebyshev spectral element collocation method
- A note on partial pivoting and Gaussian elimination
- A practical guide to splines
- Orthogonal spline collocation methods for biharmonic problems
- Fast algorithms for high-order spline collocation systems
- Parallel stable compactification for ODEs with parameters and multipoint conditions
- A parallel version of the cyclic reduction algorithm on a hypercube
- Stable parallel elimination for boundary value ODEs
- Mesh selection for stiff two-point boundary value problems
- Orthogonal spline collocation methods for Schrödinger-type equations in one space variable
- Cyclic reduction and FACR methods for piecewise Hermite bicubic orthogonal spline collocation
- The solution of nonlinear Schrödinger equations using orthogonal spline collocation
- Efficient orthogonal spline collocation methods for solving linear second order hyperbolic problems on rectangles
- A fast solver for the orthogonal spline collocation solution of the biharmonic Dirichlet problem on rectangles
- Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions
- An efficient direct method for fully conforming spectral collocation schemes
- Collocation methods for parabolic equations in a single space variable. Based on C\(^1\)-piecewise-polynomial spaces
- A high order direct method for solving Poisson's equation in a disc
- Geometric methods for computing invariant manifolds
- Convergence and instability in PCG methods for bordered systems
- An automatic continuation strategy for the solution of singularly perturbed linear two-point boundary value problems
- High performance solution of partial differential equations discretized using a Chebyshev spectral collocation method
- Parallel solution of almost block diagonal systems on a hypercube
- Implementation issues in solving nonlinear equations for two-point boundary value problems
- ORTHOGONAL CUBIC SPLINE COLLOCATION SOLUTION OF UNDERWATER ACOUSTIC WAVE PROPAGATION PROBLEMS
- Tensor Product Generalized ADI Methods for Separable Elliptic Problems
- On Spline Basis Selection for Solving Differential Equations
- A Cyclic Reduction Approach to the Numerical Solution of Boundary Value ODEs
- A coupled double splitting ADI scheme for the first biharmonic using collocation
- The Reformulation and Numerical Solution of Certain Nonclassical Initial-Boundary Value Problems
- Staircase Matrices and Systems
- On solving almost block diagonal (staircase) linear systems
- On the $H^{ - 1} $-Galerkin Method for Second-Order Linear Two-Point Boundary Value Problems
- A Deferred Correction Method for Nonlinear Two-Point Boundary Value Problems: Implementation and Numerical Evaluation
- Efficiency of Methods for Second-Order Problems
- Adaptation of a Two-Point Boundary Value Problem Solver to a Vector-Multiprocessor Environment
- FORTRAN Packages for Solving Certain Almost Block Diagonal Linear Systems by Modified Alternate Row and Column Elimination
- An Adaptive Boundary Value Runge–Kutta Solver for First Order Boundary Value Problems
- The Close Relationships between Methods for Solving Two-Point Boundary Value Problems
- An extended set of FORTRAN basic linear algebra subprograms
- On the Numerical Integration of Nonlinear Two-Point Boundary Value Problems Using Iterated Deferred Corrections. Part 2: The Development and Analysis of Highly Stable Deferred Correction Formulae
- Wrap-around partitioning for block bidiagonal linear systems
- Algorithm 540: PDECOL, General Collocation Software for Partial Differential Equations [D3]
- SOLVEBLOK: A Package for Solving Almost Block Diagonal Linear Systems
- Algorithm 546: SOLVEBLOK [F4]
- Collocation Software for Boundary-Value ODEs
- Reformulation of Boundary Value Problems into “Standard” Form
- Stable Solvers and Block Elimination for Bordered Systems
- Alternating Direction Collocation for Separable Elliptic Partial Differential Equations
- Fast Direct Solvers for Piecewise Hermite Bicubic Orthogonal Spline Collocation Equations
- Stable Parallel Algorithms for Two-Point Boundary Value Problems
- Mixed block elimination for linear systems with wider borders
- Domain-imbedding alternating direction method for linear elliptic equations on irregular regions using collocation
- Analysis of alternating direction collocation methods for parabolic and hyperbolic problems in two space variables
- Bounds for Rounding Errors in the Gaussian Elimination for Band Systems
- Alternate Row and Column Elimination for Solving Certain Linear Systems
- An Adaptive Finite Difference Solver for Nonlinear Two-Point Boundary Problems with Mild Boundary Layers
- Midpoint difference method for analysing beam structures
- A note on the efficient implementation of certain Padé Methods for linear parabolic problems
- A second-order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation
- Stability and performance analysis of a block elimination solver for bordered linear systems
- An Orthogonal Spline Collocation Alternating Direction Implicit Crank--Nicolson Method for Linear Parabolic Problems on Rectangles
- Orthogonal collocation solution of biharmonic equations
- NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (I): BIFURCATION IN FINITE DIMENSIONS
- Algorithm 688: EPDCOL
- The solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions
- Algorithm 704: ABDPACK and ABBPACK-FORTRAN programs for the solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions
- Discrete-time Orthogonal Spline Collocation Methods for Schrödinger Equations in Two Space Variables
- Numerical integration of non-linear two-point boundary-value problems using iterated deferred corrections—I
- Matrix Decomposition Algorithms in Orthogonal Spline Collocation for Separable Elliptic Boundary Value Problems
- Fourier Matrix Decomposition Methods for the Least Squares Solution of Singular Neumann and Periodic Hermite Bicubic Collocation Problems
- Iterative Algorithms for Orthogonal Spline Collocation Linear Systems
- Computation and parametrization of periodic and connecting orbits
- Runge–Kutta Software with Defect Control for Boundary Value ODE<scp>s</scp>
- Block Iterative Algorithms for Solving Hermite Bicubic Collocation Equations
- Alternating direction collocation for irregular regions
- A Collection of Problems for Which Gaussian Elimination with Partial Pivoting is Unstable
- Some relationships between implicit Runge-Kutta, collocation and Lanczosτ methods, and their stability properties
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