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Volume 9, Issue 4
Solving Boundary Value Problems for the Matrix Equation $X^{(2)}(t)-AX(t)=F(t)$

Lucas Jódar & E. Navarro

J. Comp. Math., 9 (1991), pp. 305-313.

Published online: 1991-09

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  • Abstract

In this paper we present a method for solving the matrix differential equation $X^{(2)}(t)-AX(t)=F(t)$, without increasing the dimension of the problem. By introducing the concept of co-square root of a matrix, existence and uniqueness conditions for solutions of boundary value problems related to the equation as well as explicit solutions of these solutions are given, even for the case where the matrix $A$ has no square roots.

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@Article{JCM-9-305, author = {Jódar , Lucas and Navarro , E.}, title = {Solving Boundary Value Problems for the Matrix Equation $X^{(2)}(t)-AX(t)=F(t)$}, journal = {Journal of Computational Mathematics}, year = {1991}, volume = {9}, number = {4}, pages = {305--313}, abstract = {

In this paper we present a method for solving the matrix differential equation $X^{(2)}(t)-AX(t)=F(t)$, without increasing the dimension of the problem. By introducing the concept of co-square root of a matrix, existence and uniqueness conditions for solutions of boundary value problems related to the equation as well as explicit solutions of these solutions are given, even for the case where the matrix $A$ has no square roots.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9405.html} }
TY - JOUR T1 - Solving Boundary Value Problems for the Matrix Equation $X^{(2)}(t)-AX(t)=F(t)$ AU - Jódar , Lucas AU - Navarro , E. JO - Journal of Computational Mathematics VL - 4 SP - 305 EP - 313 PY - 1991 DA - 1991/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9405.html KW - AB -

In this paper we present a method for solving the matrix differential equation $X^{(2)}(t)-AX(t)=F(t)$, without increasing the dimension of the problem. By introducing the concept of co-square root of a matrix, existence and uniqueness conditions for solutions of boundary value problems related to the equation as well as explicit solutions of these solutions are given, even for the case where the matrix $A$ has no square roots.

Lucas Jódar & E. Navarro. (1970). Solving Boundary Value Problems for the Matrix Equation $X^{(2)}(t)-AX(t)=F(t)$. Journal of Computational Mathematics. 9 (4). 305-313. doi:
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