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The paper proposes an efficient and insightful approach for solving neutral delay differential equations (NDDE) with high-frequency inputs. This paper aims to overcome the need to use a very small time step when high frequencies are present. High-frequency signals abound in communication circuits when modulated signals are involved.

The method involves an asymptotic expansion of the solution and each term in the expansion can be determined either from NDDE without oscillatory inputs or recursive equations. Such an approach leads to an efficient algorithm with a performance that improves as the input frequency increases.

An example shall indicate the salient features of the method. Its improved performance shall be shown when the input frequency increases. The example is chosen as it is similar to that in literature concerned with partial element equivalent circuit (PEEC) circuits (Bellen et al., 1999). Its structure shall also be shown to enable insights into the behaviour of the system governed by the differential equation.

The method is novel in its application to NDDE as arises in engineering applications such as those involving PEEC circuits. In addition, the focus of the method is on a technique suitable for high-frequency signals.

The purpose of this study is to address the extended travel time caused by dwelling time at stations for passengers on traditional rail transit lines. To mitigate this issue, the authors propose the “Non-stop” design, which involves trains comprised of modular vehicles that can couple and uncouple from each other during operation, thereby eliminating dwelling time at stations..

The main contributions of this paper are threefold: first, to introduce the concept of non-stop rail transit lines, which, to the best of the authors’ knowledge, has not been researched in the literature; second, to develop a framework for the operation schedule of such a line; and third, the author evaluate the potential of its implementation in terms of total passenger travel time.

The total travel time was reduced by 6% to 32.91%. The results show that the savings were more significant for long commutes and low train occupancy rates.

The non-stop system can improve existing lines without the need for the construction of additional facilities, but it requires technological advances for rolling stock.

To eliminate dwelling time at stations, the authors present the “Non-stop” design, which is based on trains composed of locomotives that couple and uncouple from each other during operation, which to the best of the authors’ knowledge has not been researched in the literature.