Improving the Efficiency of Matrix Operations in the Numerical Solution of Stiff Ordinary Differential Equations

DOI10.1145/355780.355784zbMath0382.65029OpenAlexW2056478390MaRDI QIDQ4160329

Publication date: 1978

Published in: ACM Transactions on Mathematical Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1145/355780.355784

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (40)

Parallel algorithms for solving large linear systems ⋮ The polynomial solution to the Sylvester matrix equation ⋮ Relaxed Newton-like methods for stiff differential systems ⋮ A variable parameter embedded DIRK algorithm for the numerical integration of stiff systems of ODEs ⋮ On positive-definite and skew-Hermitian splitting iteration methods for continuous Sylvester equation \(AX+XB=C\) ⋮ The Modified Newton Method in the Solution of Stiff Ordinary Differential Equations ⋮ A matrix CRS iterative method for solving a class of coupled Sylvester-transpose matrix equations ⋮ The numerical solution of large systems of stiff IVPs for ODEs ⋮ Parallel methods for ordinary differential equations ⋮ The Unified Frame of Alternating Direction Method of Multipliers for Three Classes of Matrix Equations Arising in Control Theory ⋮ A new version of successive approximations method for solving Sylvester matrix equations ⋮ An efficient algorithm for solving general coupled matrix equations and its application ⋮ Extended Arnoldi methods for large low-rank Sylvester matrix equations ⋮ Symmetric least squares solution of a class of Sylvester matrix equations via MINIRES algorithm ⋮ Design and implementation of DIRK integrators for stiff systems ⋮ Small-sample statistical condition estimation of large-scale generalized eigenvalue problems ⋮ A NEW VERSION OF THE SMITH METHOD FOR SOLVING SYLVESTER EQUATION AND DISCRETE-TIME SYLVESTER EQUATION ⋮ A note on the exponential fitting of blended, extended linear multistep methods ⋮ Analysis of trajectory errors in integrating ordinary differential equations ⋮ Embedded dirk methods for the numerical integration of stiff systems of odes ⋮ Refinement methods for state estimation via Sylvester-observer equation ⋮ A preconditioned block Arnoldi method for large Sylvester matrix equations ⋮ Some schemes for the implementation of implicit Runge-Kutta methods ⋮ A preconditioned iteration method for solving Sylvester equations ⋮ Piecewise interpolants on matrix Lie groups ⋮ Low rank solution of data‐sparse Sylvester equations ⋮ Analysis of the solution of the Sylvester equation using low-rank ADI with exact shifts ⋮ Solving stable Sylvester equations via rational iterative schemes ⋮ Developing BiCOR and CORS methods for coupled Sylvester-transpose and periodic Sylvester matrix equations ⋮ A note on the efficient solution of matrix pencil systems ⋮ Bibliography on the evaluation of numerical software ⋮ Methods for the solution ofAXD−BXC=E and its application in the numerical solution of implicit ordinary differential equations ⋮ Recent advances in methods for numerical solution of O.D.E. initial value problems ⋮ On the generalized bisymmetric and skew-symmetric solutions of the system of generalized Sylvester matrix equations ⋮ On the ADI method for Sylvester equations ⋮ The updating technique for the solution of a sequence of linear equations ⋮ A block QR algorithm for partitioning stiff differential systems ⋮ Phase properties of high order, almost P-stable formulae ⋮ On the use of parallel processors for implicit Runge-Kutta methods ⋮ A note on the Enright updating technique

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