A new amplification-fitting approach in Newton-Cotes rules to tackling the high-frequency IVPs

In this paper, we will further strengthen the fitting technique of the well-known Newton-Cotes rules. First, we fit Boole's rule using the found amplification factor, and then we use it to numerically solve first-order differential equations with oscillating solutions. If the Hamiltonian energy of the system remains almost constant then we investigate whether the new amplification-fitted methods can be used as symplectic methods for numerical integration.

The obtained results show the high accuracy of the new amplification-fitting Boole's rule-based methods.