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

Lin, Chialiang; Hsu, Chieh-Wen; Simos, T. E.; Tsitouras, Ch.

Appl. Comput. Math. 18, No. 3, 296-304 (2019).

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

Keywords:

initial value problem; multi-step methods; explicit methods; constant coefficients