SOLVING A HIGHER-ORDER LINEAR DISCRETE SYSTEMS

In this paper there is considered a linear discrete homogenous system of the order (m + 2): Delta(2)x(k) + B(2)x(k - m) = f(k), k is an element of N-0, where B is a constant n x n regular matrix, m is an element of N-0 and x: {-m, m + 1, ...} -> R-n, f: Z(0)(infinity) -> R-n. Two linearly independent solutions will be found as special matrix functions called delayed discrete cosine and delayed discrete sine. Formulas for solutions are gotten utilizing these matrix functions. An example illustrating results is given as well.