Explicit, ninth order, two step methods for solving inhomogeneous linear problems x(t) = Λx(t) plus f(t)

Here we consider the second order Inhomogeneous Linear Initial Value Problems with constant coefficients. Two-step hybrid methods (i.e. of Numerov-type) are considered for addressing this problem. A special set of order conditions is given and solved for derivation a low cost new method. Actually, we manage to save one stage (function evaluation) per step for this type of problems in comparison with the best existed methods. This is crucial as demonstrated in various numerical tests where our new proposal outperforms standard methods in the relevant literature. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.