Accurate dense output formula for exponential integrators using the scaling and squaring method. (May 2015)

• Record Type: Journal Article
• Authors: Wang, Chengshan; Fu, Xiaopeng; Li, Peng; Wu, Jianzhong
• Is Part Of: Applied mathematics letters. Volume 43(2015:May)
• Page Start: 101
• Page End: 107
• Publication Date: 2015-05
• Subjects: Exponential integrator -- Dense output formula -- Matrix exponential; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2014.12.008
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: This paper proposes an accurate dense output formula for exponential integrators. The computation of matrix exponential function is a vital step in implementing exponential integrators. By scrutinizing the computational process of matrix exponentials using the scaling and squaring method, valuable intermediate results in this process are identified and then used to establish a dense output formula. Efficient computation of dense outputs by the proposed formula enables time integration methods to set their simulation step sizes more flexibly. The efficacy of the proposed formula is verified through numerical examples from the power engineering field.