11th WSEAS International Conference on Applied Mathematics, Texas, United States Of America, 22 - 24 March 2007, pp.250-252
One can use power series expansions in the solution of the first order linear vector differential equations as long as the expansion is realized around a regular point of the differential equation. However the utilizability and the practicality of the expansion depends on the structure of the recursion amongst the coefficents of the expansion and the most preferable case uses a first order (two term) recursion. If the coefficient matrix of the equation is a polynomial then the recursion between the certain consecutive coefficients remains finite but its order is generally higher than one. Although there are various tools to handle this situation it is better to change the structure of the equation by defining new unknowns and to increase its vector dimension appropriately to get a new first order linear vector differential equation with a matrix coefficient which takes us to first order recursion amongst the expansion coefficients.