مرکز منطقه ای اطلاع رساني علوم و فناوري - A time-stepping procedure for Ẋ=A<inf>1</inf>X+XA<inf>2</inf>+D, X(0)=C

DocumentCode :

834069

Title :

A time-stepping procedure for Ẋ=A1X+XA2+D, X(0)=C

Author :

Serbin, Steven M. ; Serbin, Cynthia A.

Author_Institution :

University of Tennessee, Knoxville, TN, USA

Volume :

Issue :

fYear :

1980

fDate :

12/1/1980 12:00:00 AM

Firstpage :

1138

Lastpage :

1141

Abstract :

We develop an expression for the exact solution of the matrix differential problem $\\dot{X} = A_{1} X + XA_{2} + D, X(0) = C$ based on variation of parameters and use this to devise the time-stepping relation $X(t+h)=e^{A_{1}h}{X(t)+\\int\\liminf {0}\\limsup {h}e^{-A_{1}s}De^{-A_{2}s}ds}e^{A_{2}h}$ . We modify a procedure of Van Loan to effect efficient computation of all the terms necessary to advance the solution in time according to this relation. We consider some alternatives when sparsity is a concern. A numerical example of our procedure is included.