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Solving a class of generalized Lyapunov operator differential equations without the exponential operator function.

Lucas A. Jódar Sánchez — 1990

Publicacions Matemàtiques

In this paper a method for solving operator differential equations of the type X' = A + BX + XD; X(0) = C, avoiding the operator exponential function, is given. Results are applied to solve initial value problems related to Riccati type operator differential equations whose associated algebraic equation is solvable.

An algebraic approach for solving boundary value matrix problems: existence, uniqueness and closed form solutions.

Lucas A. Jódar Sanchez — 1988

Revista Matemática de la Universidad Complutense de Madrid

In this paper we show that in an analogous way to the scalar case, the general solution of a non homogeneous second order matrix differential equation may be expressed in terms of the exponential functions of certain matrices related to the corresponding characteristic algebraic matrix equation. We introduce the concept of co-solution of an algebraic equation of the type X^2 + A1.X + A0 = 0, that allows us to obtain a method of the variation of the parameters for the matrix case and further to find...

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Solving a class of generalized Lyapunov operator differential equations without the exponential operator function.

An algebraic approach for solving boundary value matrix problems: existence, uniqueness and closed form solutions.