A family of improved Falkner-type methods for oscillatory systems

作者：Li, Jiyong^*

来源：Applied Mathematics and Computation, 2017, 293: 345-357.

DOI：10.1016/j.amc.2016.08.046

• Improved Falkner-type methods
• Oscillatory second-order differential equations
• Global error bounds

For solving general second-order initial value problems u ''(t) = f(t, u(t), u'(t)), the classical Falkner methods can date back to Falkner's work in 1936. In this paper, we propose and study a family of improved Falkner-type methods for the oscillatory system u ''(t) + Mu(t) = g(t, u(t)), where g: R x R-d -> R-d, in which the first derivative does not appear explicitly, and M is an element of R-d x d is a symmetric positive semi-definite matrix. The new methods take into account the oscillatory structures of the problem and exactly integrate the unperturbed problem u ''(t)+Mu(t) = 0. The global error bounds of the new methods are presented. Numerical experiments are performed to show that the new methods are more efficient than other effective methods appeared in the scientific literature.

• 出版日期2017-1-15
• 单位河北师范大学