A family of Anadromic numerical methods for matrix Riccati differential equations

DOI10.1090/S0025-5718-2011-02498-1zbMath1236.65080MaRDI QIDQ3117209

Ren-Cang Li, William Kahan

Publication date: 17 February 2012

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

time-invariant problemmatrix Riccati differential equationssolution singularityanadromic numerical methodgeneralized inverse relationgroup of two-sided bilinear rational functions

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (6)

GIP integrators for matrix Riccati differential equations ⋮ The asymptotic analysis of the structure-preserving doubling algorithms ⋮ Adaptive Runge-Kutta regularization for a Cauchy problem of a modified Helmholtz equation ⋮ Fourier methods for harmonic scalar waves in general waveguides ⋮ A family of Anadromic numerical methods for matrix Riccati differential equations ⋮ A structure preserving flow for computing Hamiltonian matrix exponential

Uses Software

• LAPACK
• CLAPACK
• mctoolbox
• SONEST
• CONEST

Cites Work

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• Positive definiteness in the numerical solution of Riccati differential equations
• Unconventional schemes for a class of ordinary differential equations - with applications to the Korteweg-de Vries equation
• Preserving monotonicity in the numerical solution of Riccati differential equations
• Numerical treatment of ordinary differential equations by extrapolation methods
• Riccati differential equations
• A family of Anadromic numerical methods for matrix Riccati differential equations
• Solving Ordinary Differential Equations I
• Efficient matrix-valued algorithms for solving stiff Riccati differential equations
• Constructing Riccati differential equations with known analytic solutions for numerical experiments
• Numerical integrators based on modified differential equations
• A canonical form and solution for the matrix Riccati differential equation
• Numerical integration of the differential matrix Riccati equation
• Superposition laws for solutions of differential matrix Riccati equations arising in control theory
• Recent Progress in Extrapolation Methods for Ordinary Differential Equations
• A High-Order Method for Stiff Boundary Value Problems with Turning Points
• Almost analytic representation for the solution of the differential matrix Riccati equation
• The Factorization Method for the Numerical Solution of Two Point Boundary Value Problems for Linear ODE’s
• A Riccati Transformation Method for Solving Linear BVP<scp>s</scp>. I: Theoretical Aspects
• A Riccati Transformation Method for Solving Linear BVP<scp>s</scp>. II: Computational Aspects
• FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation
• Numerical Integration of the Differential Riccati Equation and Some Related Issues
• Generalized Chandrasekhar algorithms: Time-varying models
• Partitioned Ricatti solutions and integration-free doubling algorithms
• A Natural Approach to the Numerical Integration of Riccati Differential Equations
• Composition constants for raising the orders of unconventional schemes for ordinary differential equations
• Geometric Numerical Integration
• On Extrapolation Algorithms for Ordinary Initial Value Problems
• Monotoneity Properties of Solutions of Hermitian Riccati Matrix Differential Equations
• The numerical solution of the matrix Riccati differential equation

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