Difference schemes for second-order ordinary differential equations with corrector and predictor properties

Abstract A technique for constructing a sequence of difference schemes with the properties of a corrector and a predictor for integrating systems of the second-order ordinary differential equations is presented. The sequence of schemes begins with the explicit three-point Störmer method of the second order of approximation. Each subsequent scheme also implements the Störmer method corrected with additional terms calculated through the solution of the previous scheme. The stability of the resulting schemes and the increase in the order of convergence for the first of them are carefully substantiated. The results of calculations of the test problem are presented, confirming the increase in the order of accuracy of the constructed methods.