New explicit high‐order one‐step methods for singular initial value problems. Issue 3 (23rd April 2020) - Datsko, Bohdan; Kutniv, Myroslaw; Kunynets, Andriy; Włoch, Andrzej
Summary: New explicit one‐step high‐order numerical methods (Taylor series and Runge‐Kutta methods) for singular initial value problems for second‐order nonlinear ordinary differential equations are constructed. These methods allow to calculate an approximate solution in the neighborhood of a singular point x =0 with a high‐order of accuracy. By the substitution of the independent variable, we transform the original singular initial value problem into a nonsingular one at an infinite interval. To solve this nonsingular problem, standard numerical methods with initial conditions obtained near a singular point can be used. The effectiveness of the presented approach is confirmed by numerical experiments.