A class of linear multi-step method adapted to general oscillatory second-order initial value problems

作者：Li, Jiyong^*; Wang, Xianfen; Lu, Ming

来源：Journal of Applied Mathematics and Computing, 2018, 56(1-2): 561-591.

DOI：10.1007/s12190-017-1087-2

• Adapted methods
• Oscillatory systems
• Local truncation error
• General oscillatory second-order initial value problems
• phi-functions

This paper proposes and investigates a class of new linear multi-step methods for solving general oscillatory second-order initial value problems , where M is a positive semi-definite matrix containing implicitly the frequencies of the problem. The new methods, with coefficients depending on the frequency matrix M, incorporate the special structure of the problem brought by the linear term My(t) and integrate exactly the unperturbed oscillator . This class of new methods can be viewed extensions of famous Gautschi-type methods from special oscillatory problem to general oscillatory problem. A rigorous error analysis is given and the local truncation errors of the solution and the derivative are presented. Numerical experiments show that our new methods are more efficient in comparison with the well-known high quality methods proposed in the scientific literature.

• 出版日期2018-2
• 单位河北师范大学