Block Krylov subspace methods for approximating the linear combination of φ-functions arising in exponential integrators. (August 2016)

• Record Type: Journal Article
• Authors: Cong, Yuhao; Li, Dongping
• Is Part Of: Computers & mathematics with applications. Volume 72:issue 4(2016)
• Page Start: 846
• Page End: 855
• Publication Date: 2016-08
• Subjects: φ-functions -- Exponential integrators -- Block Krylov subspace methods -- QR decomposition; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.05.031
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper we present numerical methods for computing the matrix functions arising in exponential integrators. The matrix functions are the linear combination of the form ∑ j = 0 p φ j ( A ) b j, where φ j is related to exponential function. By reducing the corresponding systems of linear ODEs with polynomial inhomogeneity based on block Krylov subspace methods, two effective exponentials of low dimension matrix are derived to approximate the objective functions. Some useful a posteriori error estimates are established. The algorithms can be combined with time-stepping strategy to satisfy the accuracy requirements under a moderate dimension of the block Krylov subspace. Several numerical experiments are presented to demonstrate the efficiency of the methods.