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

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=0pφj(A)bj, where φj 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.