New Generalized Direct Two-Step Hybrid Block Methods with All Possible Combinations of Three Off-Step Points for Solving Second Order Ordinary Differential Equations
New generalized two-step hybrid block methods with three off-step points for direct solution of second order ordinary differential equations are proposed. The locations of three off-step points in two-step interval are obtained through permutation. The main continuous schemes are derived by interpolating approximate solutions in the form of power series at two points in a two-step interval while the second derivative of the approximate solutions are collocated at all points in the given interval. Basic properties of the method such as order, zero stability, consistency and convergence are also established. The numerical results show that the developed methods produce better accuracy than several existing methods when solving the initial value problems of second order ordinary differential equations.