Computing Matrix $\varphi$-Functions Arising in Exponential Integrators

This repository contains the code used in the technical report:

A. H. Al-Mohy and X. Liu. Computing matrix φ-functions arising in exponential integrators. ArXiv:2506.01193 [math.NA], June 2025.

The code was tested in MATLAB 2024b.

The main function phi_funm.m computes phi-functions of a matrix for given indices, and the script simple_test.m runs a simple test. The directory replication/ contains required subroutines for reproducing the results in the paper.

Replicating the results

To reproduce the results in the paper, the following MATLAB toolboxes need to be installed:

• Advanpix Multiprecision Computing Toolbox

• Anymatrix

where in Anymatrix the test matrix collection

• matrices-expm

needs to be incorporated as a group.

The results presented in the manuscript can be generated by running:

>> test_main

Acknowledgments

This work was supported by the Deanship of Scientific Research at King Khalid University Research Groups Program (grant RGP. 1/318/45).

License

This project is licensed under the terms of the BSD 2-Clause "Simplified" License (SPDX-License-Identifier: BSD-2-Clause).