Integration of the exponential function of a complex quadratic form.

Elia, Michele; Taricco, Giorgio

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On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate

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In this paper explicit expressions for solutions of Cauchy problems and two-point boundary value problems concerned with the generalized Riccati matrix differential equation are given. These explicit expressions are computable in terms of the data and solutions of certain algebraic Riccati equations related to the problem. The interplay between the algebraic and the differential problems is used in order to obtain approximate solutions of the differential problem in terms of those of...