Asymptotic formulae for a particular solution of linear nonhomogeneous discrete equations

The aim of this contribution is to develop the asymptotic formulae which describe the asymptotic behaviour of a particular solution of linear nonhomogeneous differential equation Δu(k) = A(k)u(k) + g(k) if k → ∞. It is shown that asymptotic formulae are generated by partial sums of certain formal series that satisfy the given equation. A comparison with the known explicit formula for solution of the initial problem is given and, moreover, some illustrative examples are discussed. The used method of investigation is based on results published in 1].