In this paper exponentially-fitted explicit modified Runge-Kutta type method denoted as EFMRKT for solving y'''(x) = f(x, y, y') is derived. The idea presented is based on the Simos and Berghe approach which exactly integrates initial value problems whose solutions are linear combinations of the set functions ewx and e−wx with w ∈ R the principal frequency of the problem. We developed the new EFMRKT three-stage fourth-order method called EFRKTG4 for solving third-order initial value problems. The numerical results…