  This paper considers computing partial eigenpairs of differential eigenvalue
problems (DEPs) such that eigenvalues are in a certain region on the complex
plane. Recently, based on a "solve-then-discretize" paradigm, an operator
analogue of the FEAST method has been proposed for DEPs without discretization
of the coefficient operators. Compared to conventional "discretize-then-solve"
approaches that discretize the operators and solve the resulting matrix
problem, the operator analogue of FEAST exhibits much higher accuracy; however,
it involves solving a large number of ordinary differential equations (ODEs).
In this paper, to reduce the computational costs, we propose operation
analogues of Sakurai-Sugiura-type complex moment-based eigensolvers for DEPs
using higher-order complex moments and analyze the error bound of the proposed
methods. We show that the number of ODEs to be solved can be reduced by a
factor of the degree of complex moments without degrading accuracy, which is
verified by numerical results. Numerical results demonstrate that the proposed
methods are over five times faster compared with the operator analogue of FEAST
for several DEPs while maintaining almost the same high accuracy. This study is
expected to promote the "solve-then-discretize" paradigm for solving DEPs and
contribute to faster and more accurate solutions in real-world applications.
