Numerical procedures based on Runge-Kutta methods for solving isospectral flows

DOI10.1016/S0168-9274(97)00051-2zbMath0904.65074MaRDI QIDQ1375437

Luciano Lopez, Tiziano Politi

Publication date: 26 January 1999

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

zbMATH Keywords

numerical examplesisospectral flowsLax systemsGauss-Legendre-Runge-Kutta methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Dynamics induced by flows and semiflows (37C10) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items

One step semi-explicit methods based on the Cayley transform for solving isospectral flows, Numerical methods for Hermitian unitary differential systems, On the numerical integration of orthogonal flows with Runge-Kutta methods, Applications of the Cayley approach in the numerical solution of matrix differential systems on quadratic groups

Cites Work

• Unnamed Item
• Time-stepping and preserving orthonormality
• Theory of nonlinear lattices
• Scaled Toda-like flows
• Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems
• Stability of Runge-Kutta Methods for Trajectory Problems
• Ordinary Differential Equations and the Symmetric Eigenvalue Problem
• Differential Equations and the $QR$ Algorithm
• Natural Continuous Extensions of Runge-Kutta Methods
• Finitely many mass points on the line under the influence of an exponential potential -- an integrable system
• Unitary Integrators and Applications to Continuous Orthonormalization Techniques
• Numerical Gradient Algorithms for Eigenvalue and Singular Value Calculations
• Numerical solution of isospectral flows
• The Toda lattice. II. Existence of integrals
• Integrals of nonlinear equations of evolution and solitary waves
• Runge-Kutta methods for orthogonal and isospectral flows