Abstract
A new optimized two-step hybrid block method for the numerical integration of general second-order initial value problems is presented. The method considers two intra-step points which are selected adequately in order to optimize the local truncation errors of the main formulas for the solution and the derivative at the final point of the block. The new method is zero-stable and consistent with fifth algebraic order. Numerical experiments used revealed the superiority of the new method for solving this kind of problems, in comparison with methods of similar characteristics in the literature.
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