An adaptive integrating factor midpoint method for second order evolution equations
Numerical Analysis
2026-03-03 v1 Numerical Analysis
Abstract
In this paper, we consider the integrating factor midpoint method for wave-type equations and derive optimal order a posteriori error estimates. We first introduce an integrating factor midpoint approximation defined by the piecewise linear approximate solutions, and derive suboptimal order residual-based error estimates using the energy technique. Hence the key is introducing a continuous, piecewise quadratic time reconstruction to establish optimal order error bounds. Based on the reliable a posteriori error control, we develop an adaptive time-stepping strategy. Numerical examples are implemented to verify the convergence rate of an error estimator and the high efficiency of the adaptive algorithm.
Cite
@article{arxiv.2603.00594,
title = {An adaptive integrating factor midpoint method for second order evolution equations},
author = {Xianfa Hu and Fazhan Geng and Wansheng Wang},
journal= {arXiv preprint arXiv:2603.00594},
year = {2026}
}