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

Revista Matemática de la Universidad Complutense de Madrid (1988)

- Volume: 1, Issue: 1-2-3, page 145-155
- ISSN: 1139-1138

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topJódar Sanchez, Lucas A.. "An algebraic approach for solving boundary value matrix problems: existence, uniqueness and closed form solutions.." Revista Matemática de la Universidad Complutense de Madrid 1.1-2-3 (1988): 145-155. <http://eudml.org/doc/43152>.

@article{JódarSanchez1988,

abstract = {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 existence, uniqueness conditions for solutions of boundary value problems. These conditions are of algebraic type, involving the Penrose-Moore pseudoinverse of a matrix related to the problem. A computable closed form for solutions of the problem is given.},

author = {Jódar Sanchez, Lucas A.},

journal = {Revista Matemática de la Universidad Complutense de Madrid},

keywords = {Ecuaciones diferenciales ordinarias; Ecuaciones matriciales; Problema de contorno; Modelo algebraico; Soluciones; nonhomogeneous second order matrix differential equation; co-solution},

language = {eng},

number = {1-2-3},

pages = {145-155},

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

url = {http://eudml.org/doc/43152},

volume = {1},

year = {1988},

}

TY - JOUR

AU - Jódar Sanchez, Lucas A.

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

JO - Revista Matemática de la Universidad Complutense de Madrid

PY - 1988

VL - 1

IS - 1-2-3

SP - 145

EP - 155

AB - 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 existence, uniqueness conditions for solutions of boundary value problems. These conditions are of algebraic type, involving the Penrose-Moore pseudoinverse of a matrix related to the problem. A computable closed form for solutions of the problem is given.

LA - eng

KW - Ecuaciones diferenciales ordinarias; Ecuaciones matriciales; Problema de contorno; Modelo algebraico; Soluciones; nonhomogeneous second order matrix differential equation; co-solution

UR - http://eudml.org/doc/43152

ER -

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