Journal of Mathematical Chemistry ( IF 1.81 ) Pub Date : 2019-11-15 , DOI: 10.1007/s10910-019-01074-5
Ch. Tsitouras

A family of explicit, semi-symmetric, eighth-order, six-step methods for the numerical solution of $$y^{\prime \prime }=f(x,y)$$ is considered. This family can be derived through interpolation techniques and only two stages (function evaluations) are spent per step. A method is given with variable coefficients. This variance is based in the requirement to nullify the errors when solving the standard simple oscillator. We conclude with numerical tests over a set of problems justifying our effort of dealing with the new method.

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