## Explicit, semi-symmetric, hybrid, six-step, eighth order methods for solving $$y''=f(x,y)$$.(English)Zbl 1431.65096

Summary: A family of explicit, semi-symmetric, eighth-order, six-step methods for the numerical solution of $$y''=f(x,y)$$ is studied. This family can be derived through interpolation techniques and only two function evaluations are spent per step. An interval of periodicity is possessed and the phase-lag is of high order. We conclude with numerical tests over a set of problems justifying our effort of dealing with the new methods.

### MSC:

 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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