ARTICLE | doi:10.20944/preprints202211.0023.v1
Subject: Mathematics & Computer Science, Numerical Analysis & Optimization Keywords: Taylor; exponentially-fitted; two-parameter; periodic; oscillatory; frequency
Online: 1 November 2022 (07:29:50 CET)
Classical numerical methods for solving ordinary differential equations often produce less accurate results when applied to problems with oscillatory or periodic behaviour. To adapt them for such problems, they are usually modified using the exponential fitting technique. This adaptation allows for the construction of new methods from their classical counterparts. The new methods are usually more accurate, efficient and suitable for handling the oscillatory or periodic behaviour of the problem. In this work, we construct a two-parameter exponentially-fitted Taylor method suitable for solving oscillatory or periodic problems that possess two frequencies. The construction algorithm is based on a proposed six-step flowchart discussed by authors in related literature. Two standard test problems were used to illustrate the accuracy and performance of the proposed method.
ARTICLE | doi:10.20944/preprints202206.0387.v1
Subject: Mathematics & Computer Science, Computational Mathematics Keywords: Exponentially–fitted; Obrechkoff; Fourth–derivative; Oscillatory; Periodic; Single–step
Online: 28 June 2022 (12:50:23 CEST)
The quest for accurate and more efficient methods for solving periodic/oscillatory problems is gaining more attention in recent time. This paper presents the construction and implementation of a family of exponentially–fitted Obrechkoff methods. A single–step Obrechkoff method involving terms up to the fourth derivatives was used as the base method. We also present the stability and convergence properties of the constructed family of methods. Two numerical examples were use to illustrate the performance of the constructed methods.
ARTICLE | doi:10.20944/preprints202103.0592.v1
Subject: Engineering, Electrical & Electronic Engineering Keywords: Electric Vehicles; batch reinforcement learning; dueling neural networks; fitted Q-iteration
Online: 24 March 2021 (13:44:36 CET)
We consider the problem of coordinating the charging of an entire fleet of electric vehicles (EV), using a model-free approach, i.e. purely data-driven reinforcement learning (RL). The objective of the RL-based control is to optimize charging actions, while fulfilling all EV charging constraints (e.g. timely completion of the charging). In particular, we focus on batch-mode learning and adopt fitted Q-iteration (FQI). A core component in FQI is approximating the Q-function using a regression technique, from which the policy is derived. Recently, a dueling neural networks architecture was proposed and shown to lead to better policy evaluation in the presence of many similar-valued actions, as applied in a computer game context. The main research contributions of the current paper are that (i)we develop a dueling neural networks approach for the setting of joint coordination of an entire EV fleet, and (ii)we evaluate its performance and compare it to an all-knowing benchmark and an FQI approach using EXTRA trees regression technique, a popular approach currently discussed in EV related works. We present a case study where RL agents are trained with an epsilon-greedy approach for different objectives, (a)cost minimization, and (b)maximization of self-consumption of local renewable energy sources. Our results indicate that RL agents achieve significant cost reductions (70--80%) compared to a business-as-usual scenario without smart charging. Comparing the dueling neural networks regression to EXTRA trees indicates that for our case study's EV fleet parameters and training scenario, the EXTRA trees-based agents achieve higher performance in terms of both lower costs (or higher self-consumption) and stronger robustness, i.e. less variation among trained agents. This suggests that adopting dueling neural networks in this EV setting is not particularly beneficial as opposed to the Atari game context from where this idea originated.
ARTICLE | doi:10.20944/preprints201607.0018.v1
Subject: Mathematics & Computer Science, Numerical Analysis & Optimization Keywords: Exponentially-fitted method, interpolation, collocation, stability properties, continuous method, stiff problems
Online: 11 July 2016 (08:15:27 CEST)
In this paper, we consider the development of algorithms for the solution of first order initial value problems whose solution exhibits exponential behaviour. Method of interpolation and collocation of basis function to give system of nonlinear equations which is solved for the unknown parameters to give a continuous scheme. The discrete methods recovered from the continuous scheme are implemented in block form. The stability properties of the method is verified and numerical experiments show that our method is efficient in handling these problems