Journal Article10.1016/0168-9274(93)90041-O
A parallel direct method for solving initial value problems for ordinary differential equations
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TL;DR: The obtained block tridiagonal systems are solved by generalization of the parallel cyclic reduction, and it is shown that direct methods give good results for problems of small dimension.
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About: This article is published in Applied Numerical Mathematics. The article was published on 01 Jan 1993. The article focuses on the topics: Tridiagonal matrix algorithm & Tridiagonal matrix.
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Citations
Boundary value methods based on Adams-type methods
TL;DR: In this article, the authors derive boundary value methods based on k-step Adams-type methods for the solution of initial value problems and prove that the choice of boundary conditions, instead of the usual initial conditions, improves the stability properties of the classical Adams methods.
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Stability of some boundary value methods for the solution of initial value problems
TL;DR: In this article, the stability properties of boundary value methods (BVMs) for the solution of initial value problems are investigated. But the authors focused on the BVMs based on the midpoint rule, on the Simpson method and on an Adams method of order 3.
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Stability and convergence of boundary value methods for solving ODE
P. Marzulli,Donato Trigiante +1 more
TL;DR: In this article, the authors review some recent approaches to the numerical solution of ODE based on the solution of IVP (Initial Value Problem) by means of suitable BVM (Boundary Value Methods).
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Stability properties of some boundary value methods
Luigi Brugnano,Donato Trigiante +1 more
TL;DR: The stability properties of three particular BVMs when used for solving linear systems of ODEs and an efficient implementation of these methods are described.
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Boundary value methods for the solution of differential-algebraic equations
TL;DR: In this article, the same techniques are applied to the solution of linear initial value problems of DAEs, and convergence results are stated in the case of constant coefficients, and numerical examples are given on linear time-varying problems.
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References
•Book
Introduction to Parallel and Vector Solution of Linear Systems
J. M. Ortega
- 30 Apr 1988
TL;DR: The Conjugate Gradient Algorithm and the Iterative Methods for Linear Equations are described, which simplify the derivation of linear algebra to simple linear algebra.
649
Solving narrow banded systems on ensemble architectures
TL;DR: The arithmetic and communicationcomplexity of Gaussian elimination and block cyclic reduction for the solution of the reduced system on boolean cubes, perfect shuffle and shuffle-exchange networks, binary trees, and linear arrays is investigated.
63
Boundary value methods and BV-stability in the solution of initial value problems
Luciano Lopez,Donato Trigiante +1 more
TL;DR: In this article, boundary value techniques based on a three-term numerical method for solving initial value problems were investigated and the notions of BV-stability and BVrelative stability were introduced in order to clarify the conditions that a 3-term scheme must satisfy for solving efficiently initial-value problems.
32
Parallel factorizations and parallel solvers for tridiagonal linear systems
Pierluigi Amodio,Luigi Brugnano +1 more
TL;DR: By means of this concept the concept of parallel factorization is formalized as a set of scalar factorizations and is able to give a unified approach to the problem of solving tridiagonal linear systems on parallel computers.
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A multilevel parallel solver for block tridiagonal and banded linear systems
Ibrahim N. Hajj,Stig Skelboe +1 more
- 01 Sep 1990
TL;DR: It is demonstrated how the efficiency of the general block tridiagonal multilevel algorithm can be improved by introducing the equivalent of two-way Gaussian elimination for the first and the last partitioning and by carefully balancing the load of the processors.