An explicit four-step phase-fitted method for the numerical integration of second-order initial-value problems
This paper is concerned with the numerical solution of initial value problems for special second-order equations i.e. \(y'' = f(x,y)\), by means of linear multistep methods. A family of four-step explicit methods with a free parameter and local truncation error of order six is presented. It is shown that by choosing appropriately the free parameter it is possible to get a method which has a phase-lag of infinite order and an interval of periodicity \((0, H^ 2_ 0)\) with \(H_ 0 \cong 4.40\). This means that for the linear test equation \(y'' + k^ 2 y = 0\) and a fixed stepsize \(h\) such that \(0 < hk < H_ 0\) the numerical method exhibits the same periodic behaviour as the exact solution. Finally, the numerical experiments obtained with four test problems are presented to confirm the expected behaviour of the method.
scientific article; zbMATH DE number 758523
scientific article