The numerical solution of the matrix Riccati differential equation

1973 ◽  
Vol 18 (1) ◽  
pp. 71-73 ◽  
Author(s):  
E. Davison ◽  
M. Maki
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Riccati Differential Equation ◽  
The Matrix

scholarly journals A special property of the matrix Riccati equation

1974 ◽  
Vol 10 (2) ◽  
pp. 245-253 ◽  
Author(s):  
A.N. Stokes
Keyword(s):  
Differential Equation ◽  
Riccati Equation ◽  
Symmetric Matrix ◽  
Special Property ◽  
Positive Definiteness ◽  
Symmetric Matrices ◽  
Unusual Property ◽  
Riccati Differential Equation ◽  
The Matrix ◽  
Independent Variable

In the domain of real symmetric matrices ordered by the positive definiteness criterion, the symmetric matrix Riccati differential equation has the unusual property of preserving the ordering of its solutions as the independent variable changes, Here is is shown that, subject to a continuity restriction, the Riccati equation is unique among comparable equations in possessing this property.

scholarly journals A canonical form and solution for the matrix Riccati differential equation

1985 ◽  
Vol 26 (3) ◽  
pp. 355-361 ◽  
Author(s):  
R. B. Leipnik
Keyword(s):  
Differential Equation ◽  
Steady State ◽  
Canonical Form ◽  
The Self ◽  
State Equations ◽  
Riccati Differential Equation ◽  
Adjoint Matrix ◽  
Transient Problem ◽  
The Matrix ◽  
Constant Coefficients

AbstractA canonical form of the self-adjoint Matrix Riccati Differential Equation with constant coefficients is obtained in terms of extremal solutions of the self-adjoint Matrix Riccati Algebraic (steady-state) Equations. This form is exploited in order to obtain a convenient explicit solution of the transient problem. Estimates of the convergence rate to the steady state are derived.

scholarly journals Accessibility of the matrix Riccati differential equation

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 4130031-4130032
Author(s):  
G. Dirr ◽  
U. Helmke
Keyword(s):  
Differential Equation ◽  
Riccati Differential Equation ◽  
The Matrix

Relative error analysis of matrix exponential approximations for numerical integration

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Stefano Maset
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Numerical Solution ◽  
Relative Error ◽  
Absolute Error ◽  
Linear Ordinary Differential Equation ◽  
Matrix Exponential ◽  
Initial Value ◽  
The Matrix ◽  
Long Time

AbstractIn this paper, we study the relative error in the numerical solution of a linear ordinary differential equation y′(t) = Ay(t), t ≥ 0, where A is a normal matrix. The numerical solution is obtained by using at any step an approximation of the matrix exponential, e.g. a polynomial or a rational approximation. The error of the numerical solution with respect to the exact solution is due to this approximation as well as to a possible perturbation in the initial value. For an unperturbed initial value, we find: 1) unlike the absolute error, the relative error always grows linearly in time; 2) in the long-time, the contributions to the relative error relevant to non-rightmost eigenvalues of A disappear.

scholarly journals Optimization Algorithm of Matrix Riccati Differential Equation and Application

2011 ◽  
Vol 2-3 ◽  
pp. 801-806
Author(s):  
Xiang Lin Hou ◽  
De Sheng Huang ◽  
Cong Chen
Keyword(s):  
Differential Equation ◽  
Matrix Element ◽  
Optimization Method ◽  
Control Parameters ◽  
Riccati Differential Equation ◽  
Dynamic Design ◽  
Design Variables ◽  
The Matrix ◽  
New Thinking ◽  
Riccati Matrix

To the matrix Riccati differential equation, based on dynamic design Variables Optimization Method, making unknown element of Riccati matrix as design variables, square sum of defined summation matrix element as objective function, a kind of new optimization Method about element of Riccati matrix orders is built. Universal program is formed. Practical examples are computed. Effectiveness is shown through result. The method is a new thinking for computing high order matrix Riccati Differential equation and obtaining control parameters.

Sign in / Sign up

Export Citation Format

Share Document