(untitled) (Advances in Applied Mathematics and Mechanics, 2025)
In this paper, by combining the modified one-leg θ-methods with linear interpolation, a new class of one-leg θ-methods for solving initial value problems of neutral pantograph equations with multiple delay terms is presented. Our new approach, which is based on a geometric grid, exhibits better asymptotic stability compared to traditional θ-methods. Under appropriate conditions, we prove, using the joint spectral radius method, that the proposed methods are asymptotically stable if and only if 0 < θ ≤ 1. This indicates that the new methods overcome the limitation of the traditional θ-methods, which require 12 ≤ θ ≤ 1 to ensure asymptotic stability. Furthermore, several numerical experiments are provided to validate our theoretical results.