New explicit high‐order one‐step methods for singular initial value problems. Issue 3 (23rd April 2020)

• Record Type: Journal Article
• Authors: Datsko, Bohdan; Kutniv, Myroslaw; Kunynets, Andriy; Włoch, Andrzej
• Is Part Of: Computational and mathematical methods. Volume 3:Issue 3(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-04-23
• Subjects: nonlinear ordinary differential equation -- Runge‐Kutta methods -- singular initial value problem -- Taylor series method; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1099
• Languages: English
• ISSNs: 2577-7408

Abstract

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.