Block Krylov subspace methods for approximating the linear combination of -functions arising in exponential integrators

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• 作者：Yuhao Cong^a ; ^b ; ^{yhcong@shu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Dongping Li^b ; ^c
• 关键词：φφ-functions ; Exponential integrators ; Block Krylov subspace methods ; QRQR decomposition
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：72
• 期：4
• 页码：846-855
• 全文大小：475 K

文摘

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 ${\sum }_{j=0}^p{\phi }_j\left(A\right)b_j$, where φ_j${\phi }_j$ 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.