ELLIPSOIDAL BOUNDS FOR THE SOLUTIONS OF SYSTEMS OF ORDINARY LINEAR DIFFERENTIAL EQUATIONS.
AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OHIO
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An approximate solution for a linear system of ordinary differential equations will fail to satisfy this system by some quantity called the residual. The present report derives a method for determining bounds for the error of the approximate solution from bounds on the residual. The residual and the error are characterized as vectors which lie inside and on the surface of ellipsoids. For an nth order system these ellipsoids are given by symmetric positive definite quadratic forms determined by matrices. The matrix for the residual is assumed given. A differential inequality is derived from which the matrix for the error ellipsoid is computed. The narrowness of the error bounds so obtained is studied on a theoretical basis. Author
- Theoretical Mathematics