Embedded 5(4) pair implicit 2-step hybrid method for solving special second-order initial value problems

A new embedded 5(4) pair implicit 2-step hybrid method for solving second-order differential equation of the form y" = f (x, y) is proposed in this paper. The new method is constructed by introducing single diagonal element in the order conditions. The order conditions which contain the coefficients of the method are used in the error constant to determine the free parameter in fourth and fifth order implicit 2-step hybrid method. The stability analysis is determined by the interval of periodicity and the interval of absolute stability. Some numerical experiments are tested upon and the numerical results showed that the new method is more accurate compared with the implicit 2-step hybrid method of order four and order five.