Applications of Invariant Imbedding.

Abstract

Abstract : Invariant imbedding is a method for the computational solution of two-point boundary-value problems. One common source of such problems is in the application of the method of lines, or an expansion procedure, to a system of partial differential equations. Such partial differential equations might describe, for example, the dynamic mechanics of structures such as an aircraft fuselage or a missile silo. The research conducted under this grant has been directed toward two objectives. The first objective was to improve the effectiveness and efficiency of invariant imbedding by providing means for automatically controlling the associated computational effort. The second objective was to extend the range of applicability of invariant imbedding to include singular two-point boundary-value problems. Such singular problems arise, for example, by applying the method of lines to partial differential equations in spherical or cylindrical coordinate systems. In regard to the first of these objectives, a number of different methods, which are generically termed 'relative-error monitors', have been developed and are in the process of being subjected to computational experimentation. As regards the second objective, it has been shown how to apply the method of invariant imbedding to 'homogeneous' linear two-point boundary-value problems. The further extension to inhomogeneous problems is presently being pursued. (Author)