Two-points problem for an evolutional first order equation in Banach space
Numerical Analysis
2025-05-06 v1 Numerical Analysis
Functional Analysis
Abstract
Two-points nonlocal problem for the first order differential evolution equation with an operator coefficient in a Banach space is considered. An exponentially convergent algorithm is proposed and justified in assumption that the operator coefficient is strongly positive and some existence and uniqueness conditions are fulfilled. This algorithm leads to a system of linear equations that can be solved by fixed-point iteration. The algorithm provides exponentially convergence in time that in combination with fast algorithms on spatial variables can be efficient treating such problems. The efficiency of the proposed algorithms is demonstrated by numerical examples.
Cite
@article{arxiv.1007.0174,
title = {Two-points problem for an evolutional first order equation in Banach space},
author = {T. Ju. Bohonova and V. B. Vasylyk},
journal= {arXiv preprint arXiv:1007.0174},
year = {2025}
}