Discrete Time Research Articles

Quantifying the Health–Economy Trade-Offs: Mathematical Model of COVID-19 Pandemic Dynamics

The COVID-19 pandemic has presented a complex situation that requires a balance between control measures like lockdowns and easing restrictions. Control measures can limit the spread of the virus but can also cause economic and social issues. Easing restrictions can support economic recovery but may increase the risk of virus transmission. Mathematical approaches can help address these trade-offs by modeling the interactions between factors such as virus transmission rates, public health interventions, and economic and social impacts. A study using a susceptible-infected-susceptible (SIS) model with modified discrete time was conducted to determine the cost of handling COVID-19. The results showed that, without government intervention, the number of patients rejected by health facilities and the cost of handling a pandemic increased significantly. Lockdown intervention provided the least number of rejected patients compared to social distancing, but the costs of handling the pandemic in the lockdown scenario remained higher than those of social distancing. This research demonstrates that mathematical approaches can help identify critical junctures in a pandemic, such as limited health system capacity or high transmission rates, that require rapid response and appropriate action. By using mathematical analysis, decision-makers can develop more effective and responsive strategies, considering the various factors involved in the virus’s spread and its impact on society and the economy.

A Constraint Programming Approach for Discrete Time–Cost Tradeoff Problems in a Time-Constrained Activity Network

The discrete time-cost tradeoff problem (DTCTP) is a well-researched topic in the field of operations research. The majority of existing DTCTP models are based on traditional activity networks, which permit the execution of an activity as soon as all its predecessors have been completed. This assumption is reasonable, but it is important to note that there are always exceptions. The main work of this study was threefold. Firstly, we expanded the analysis of the DTCTP to encompass time-constrained activity networks (DTCTPTC), which encompassed three different types of time constraints. The first constraint was the time-window constraint, which limited the time interval during which an activity could be executed. The second constraint was the time-schedule constraint, which specified the times at which an activity could begin execution. The third constraint was the time-switch constraint, which required project activities to start at specific times and remain inactive during designated time periods. Secondly, a constraint programming (CP) model was developed for the purpose of solving the DTCTPTC. The model employed interval variables to define the activity and its potential time constraints, while CP expressions were utilized to ensure the feasibility of the solution. The objective was to identify the optimal execution mode for each activity, the optimal start times for time-scheduled activities, and the optimal work/rest patterns for time-switch activities, with the aim of minimizing the total cost of the project. Finally, the efficacy of the proposed CP model was validated through two case studies based on two illustrative projects of varying sizes. The outcomes were then compared against existing algorithms. The results demonstrated that time constraints were important factors affecting schedule optimization, and the proposed CP model had the ability to solve large-scale DTCTPTC.

Single-cell transcriptomic profiling of human pancreatic islets reveals genes responsive to glucose exposure over 24 h.

Disruption of pancreatic islet function and glucose homeostasis can lead to the development of sustained hyperglycaemia, beta cell glucotoxicity and subsequently type 2 diabetes. In this study, we explored the effects of in vitro hyperglycaemic conditions on human pancreatic islet gene expression across 24 h in six pancreatic cell types: alpha; beta; gamma; delta; ductal; and acinar. We hypothesised that genes associated with hyperglycaemic conditions may be relevant to the onset and progression of diabetes. We exposed human pancreatic islets from two donors to low (2.8 mmol/l) and high (15.0 mmol/l) glucose concentrations over 24 h in vitro. To assess the transcriptome, we performed single-cell RNA-seq (scRNA-seq) at seven time points. We modelled time as both a discrete and continuous variable to determine momentary and longitudinal changes in transcription associated with islet time in culture or glucose exposure. Additionally, we integrated genomic features and genetic summary statistics to nominate candidate effector genes. For three of these genes, we functionally characterised the effect on insulin production and secretion using CRISPR interference to knock down gene expression in EndoC-βH1 cells, followed by a glucose-stimulated insulin secretion assay. In the discrete time models, we identified 1344 genes associated with time and 668 genes associated with glucose exposure across all cell types and time points. In the continuous time models, we identified 1311 genes associated with time, 345 genes associated with glucose exposure and 418 genes associated with interaction effects between time and glucose across all cell types. By integrating these expression profiles with summary statistics from genetic association studies, we identified 2449 candidate effector genes for type 2 diabetes, HbA1c, random blood glucose and fasting blood glucose. Of these candidate effector genes, we showed that three (ERO1B, HNRNPA2B1 and RHOBTB3) exhibited an effect on glucose-stimulated insulin production and secretion in EndoC-βH1 cells. The findings of our study provide an in-depth characterisation of the 24 h transcriptomic response of human pancreatic islets to glucose exposure at a single-cell resolution. By integrating differentially expressed genes with genetic signals for type 2 diabetes and glucose-related traits, we provide insights into the molecular mechanisms underlying glucose homeostasis. Finally, we provide functional evidence to support the role of three candidate effector genes in insulin secretion and production. The scRNA-seq data from the 24 h glucose exposure experiment performed in this study are available in the database of Genotypes and Phenotypes (dbGap; https://www.ncbi.nlm.nih.gov/gap/ ) with accession no. phs001188.v3.p1. Study metadata and summary statistics for the differential expression, gene set enrichment and candidate effector gene prediction analyses are available in the Zenodo data repository ( https://zenodo.org/ ) under accession number 11123248. The code used in this study is publicly available at https://github.com/CollinsLabBioComp/publication-islet_glucose_timecourse .

Reliability analysis and preventive maintenance policy for consecutive k$k$‐out‐of‐n:F$n: F$ balanced system under failure criterion operating in shock environment

AbstractThis paper presents a consecutive ‐out‐of‐: balance system in a shock environment, where the state transition of component is induced by external shocks. If a predetermined threshold number of effective shocks are applied to component in a critical state, the component will fail. The state of the system is defined by the number of consecutive failing component groups in the system, which leads to system failure when a critical number of consecutive failing components is reached. To minimize maintenance costs, we propose a preventive maintenance method with an optimization model. We use finite Markov chain imbedding and Phase‐type distribution to calculate component group failure rates and associated probability functions in discrete and continuous time, respectively. The validity and accuracy of the model are confirmed by numerical examples and Monte Carlo simulations.

The turnpike property for high‐dimensional interacting agent systems in discrete time

AbstractWe investigate the interior turnpike phenomenon for discrete‐time multi‐agent optimal control problems. While for continuous systems the turnpike property has been established, we focus here on first‐order discretizations of such systems. It is shown that the resulting time‐discrete system inherits the turnpike property with estimates of the same type as in the continuous case. In particular, we prove that the discrete time optimal control problem is strictly dissipative and the cheap control assumption holds.

Tensor network influence functionals in the continuous-time limit: Connections to quantum embedding, bath discretization, and higher-order time propagation

Tensor network influence functionals in the continuous-time limit: Connections to quantum embedding, bath discretization, and higher-order time propagation

Cost-effectiveness of large-panel next-generation sequencing in guiding first-line treatment decisions for patients with nonsquamous advanced non-small cell lung cancer.

Clinical practice guidelines recommend broad-panel genomic profiling to identify actionable genomic alterations for patients with advanced non-small cell lung cancer (aNSCLC). To assess the cost-effectiveness of large-panel next-generation sequencing (LP-NGS) compared with current empirical single-gene test (SGT) patterns to inform first-line treatment decisions for patients with aNSCLC from a US commercial payer perspective, accounting for the effect of testing turnaround time and time to treatment initiation. We developed a discrete-event simulation model to estimate the impact of LP-NGS vs SGT for patients with nonsquamous aNSCLC. Discrete events and timing included testing patterns, receipt of the initial test result, treatment initiation (targeted vs nontargeted therapies), switching, retesting, rebiopsies, clinical trial participation, progression on therapy, and death. LP-NGS and SGT cohorts each comprised 100,000 adults with aNSCLC simulated over a 5-year postdiagnosis period, assumed to have the same distribution of genomic alterations. The model predicted the proportion of patients receiving appropriate first-line therapy according to clinical practice guidelines. Economic outcomes included expected life-years gained, quality-adjusted life-years, and the total costs of care over 5 years. Sensitivity and scenario analyses explored the robustness of the base-case model results. In the base-case model, LP-NGS was likely to identify more alterations than SGT. Total 5-year costs per patient were $539,658 for LP-NGS and $544,550 for SGT (net difference, $4,892 lower costs per patient for LP-NGS), which is likely to be cost-effective 95.1% of the time. The most influential model parameters on the 5-year total costs of care were preprogression nondrug medical costs on nontargeted therapy, NGS turnaround time, and clinical trial participation. This study suggests that LP-NGS to guide first-line treatment decisions is clinically more appropriate (more likely to identify alterations and subsequently allocate patients to clinically appropriate therapy) and provides a dominant cost-effectiveness treatment strategy over 5 years for patients with newly diagnosed aNSCLC in the United States.

Temporal Trends in End-Tidal Capnography and Outcomes in Out-of-Hospital Cardiac Arrest

While widely measured, the time-varying association between exhaled end-tidal carbon dioxide (EtCO2) and out-of-hospital cardiac arrest (OHCA) outcomes is unclear. To evaluate temporal associations between EtCO2 and return of spontaneous circulation (ROSC) in the Pragmatic Airway Resuscitation Trial (PART). This study was a secondary analysis of a cluster randomized trial performed at multicenter emergency medical services agencies from the Resuscitation Outcomes Consortium. PART enrolled 3004 adults (aged ≥18 years) with nontraumatic OHCA from December 1, 2015, to November 4, 2017. EtCO2 was available in 1172 cases for this analysis performed in June 2023. PART evaluated the effect of laryngeal tube vs endotracheal intubation on 72-hour survival. Emergency medical services agencies collected continuous EtCO2 recordings using standard monitors, and this secondary analysis identified maximal EtCO2 values per ventilation and determined mean EtCO2 in 1-minute epochs using previously validated automated signal processing. All advanced airway cases with greater than 50% interpretable EtCO2 signal were included, and the slope of EtCO2 change over resuscitation was calculated. The primary outcome was ROSC determined by prehospital or emergency department palpable pulses. EtCO2 values were compared at discrete time points using Mann-Whitney test, and temporal trends in EtCO2 were compared using Cochran-Armitage test of trend. Multivariable logistic regression was performed, adjusting for Utstein criteria and EtCO2 slope. Among 1113 patients included in the study, 694 (62.4%) were male; 285 (25.6%) were Black or African American, 592 (53.2%) were White, and 236 (21.2%) were another race; and the median (IQR) age was 64 (52-75) years. Cardiac arrest was most commonly unwitnessed (n = 579 [52.0%]), nonshockable (n = 941 [84.6%]), and nonpublic (n = 999 [89.8%]). There were 198 patients (17.8%) with ROSC and 915 (82.2%) without ROSC. Median EtCO2 values between ROSC and non-ROSC cases were significantly different at 10 minutes (39.8 [IQR, 27.1-56.4] mm Hg vs 26.1 [IQR, 14.9-39.0] mm Hg; P < .001) and 5 minutes (43.0 [IQR, 28.1-55.8] mm Hg vs 25.0 [IQR, 13.3-37.4] mm Hg; P < .001) prior to end of resuscitation. In ROSC cases, median EtCO2 increased from 30.5 (IQR, 22.4-54.2) mm HG to 43.0 (IQR, 28.1-55.8) mm Hg (P for trend < .001). In non-ROSC cases, EtCO2 declined from 30.8 (IQR, 18.2-43.8) mm Hg to 22.5 (IQR, 12.8-35.4) mm Hg (P for trend < .001). Using adjusted multivariable logistic regression with slope of EtCO2, the temporal change in EtCO2 was associated with ROSC (odds ratio, 1.45 [95% CI, 1.31-1.61]). In this secondary analysis of the PART trial, temporal increases in EtCO2 were associated with increased odds of ROSC. These results suggest value in leveraging continuous waveform capnography during OHCA resuscitation. ClinicalTrials.gov Identifier: NCT02419573.

Observation of discrete-light temporal refraction by moving potentials with broken Galilean invariance

Refraction is a basic beam bending effect at two media’s interface. While traditional studies focus on stationary boundaries, moving boundaries or potentials could enable new laws of refractions. Meanwhile, media’s discretization plays a pivotal role in refraction owing to Galilean invariance breaking principle in discrete-wave mechanics, making refraction highly moving-speed dependent. Here, by harnessing a synthetic temporal lattice in a fiber-loop circuit, we observe discrete time refraction by a moving gauge-potential barrier. We unveil the selection rules for the potential moving speed, which can only take an integer v = 1 or fractional v = 1/q (odd q) value to guarantee a well-defined refraction. We observe reflectionless/reflective refractions for v = 1 and v = 1/3 speeds, transparent potentials with vanishing refraction/reflection, refraction of dynamic moving potential and refraction for relativistic Zitterbewegung effect. Our findings may feature applications in versatile time control and measurement for optical communications and signal processing.

Dynamical properties of a small heterogeneous chain network of neurons in discrete time

We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analysis techniques: fixed point analysis, phase portraits, Jacobian matrix, and bifurcation diagrams. We observe the coexistence of chaotic and period-4 attractors. Various codimension-1 and -2 patterns for example saddle-node, period-doubling, Neimark–Sacker, double Neimark–Sacker, flip- and fold-Neimark–Sacker, and 1 : 1 and 1 : 2 resonance are also explored. Furthermore, the study employs two synchronization measures to quantify how the oscillators in the network behave in tandem with each other over a long number of iterations. Finally, a time series analysis of the model is performed to investigate its complexity in terms of sample entropy.

Analytical Selection of Leakage Inductance for Single-Phase Dual Active Bridge Converters

The single-phase dual active bridge (DAB) DC/DC converter is a vital component in modern power electronics systems, facilitating efficient bidirectional power transfer between various energy sources and loads. One of the critical aspects in the design of such converters is the selection of an appropriate leakage inductance, as it significantly affects the circulating power within the converter. This study investigates the influence of inductance on the reactive power flow and introduces an analytical formula for calculating the necessary leakage inductance based on the specified rated power of the DAB converter. By employing the inductance values determined through the proposed formula, the developed power control-based modulation method, implemented in discrete time, successfully achieves zero reactive power caused by the first harmonic components under all load conditions. This selection of leakage inductance optimizes the performance of the converter ensuring efficient power delivery across various applications. The applicability of this method extends to various DAB applications, including electric vehicles, integration with asynchronous microgrids, and aerospace systems.

Intermittent event-triggered control for exponential synchronization of delayed neural networks on time Scales

This paper studies the exponential synchronization of delayed neural networks (DNNs) on time scales using the intermittent event-triggered control (IETC) method. Initially, considering the time scale situation, an IETC that merges intermittent control and event-triggered control is introduced, and a new differential inequality is developed. Subsequently, an exponential synchronization criterion is established based on the Lyapunov function, the proposed differential inequality and the time scale theory, applicable to continuous, discrete and hybrid time domains. Furthermore, under the event-triggered condition, it is demonstrated that the lower bound of each event-triggered interval exceeds a positive constant, thereby preventing the occurrence of Zeno’s behavior. Finally, the approach efficacy is validated through numerical examples.

Snap-back repellers and chaos in a class of discrete-time memristor circuits

In the last decade the flux-charge analysis method (FCAM) has been successfully used to show that continuous-time (CT) memristor circuits possess for structural reasons first integrals (invariants of motion) and their state space can be foliated in invariant manifolds. Consequently, they display an initial condition dependent dynamics, extreme multistability (coexistence of infinitely many attractors) and bifurcations without parameters. Recently, a new discretization scheme has been introduced for CT memristor circuits, guaranteeing that the first integrals are preserved exactly in the discretization. On this basis, FCAM has been extended to discrete-time (DT) memristor circuits showing that they also are characterized by invariant manifolds and they display extreme multistability and bifurcations without parameters. This manuscript considers the maps obtained via DT-FCAM for a circuit with a flux-controlled memristor and a capacitor and it provides a thorough and rigorous investigation of the presence of chaotic dynamics. In particular, parameter ranges are obtained where the maps have snap-back repellers at some fixed points, thus implying that they display chaos in the Marotto and also in the Li–Yorke sense. Bifurcation diagrams are provided where it is possible to analytically identify relevant points in correspondence with the appearance of snap-back repellers and the onset of chaos. The dependence of the bifurcation diagrams and snap-back repellers upon the circuit initial conditions and the related manifold is also studied.

Conditional score approaches to errors‐in‐variables competing risks data in discrete time

Analysis of competing risks data has been an important topic in survival analysis due to the need to account for the dependence among the competing events. Also, event times are often recorded on discrete time scales, rendering the models tailored for discrete‐time nature useful in the practice of survival analysis. In this work, we focus on regression analysis with discrete‐time competing risks data, and consider the errors‐in‐variables issue where the covariates are prone to measurement errors. Viewing the true covariate value as a parameter, we develop the conditional score methods for various discrete‐time competing risks models, including the cause‐specific and subdistribution hazards models that have been popular in competing risks data analysis. The proposed estimators can be implemented by efficient computation algorithms, and the associated large sample theories can be simply obtained. Simulation results show satisfactory finite sample performances, and the application with the competing risks data from the scleroderma lung study reveals the utility of the proposed methods.

Evaluating the uncertainty in mean residual times: Estimators based on residence times from discrete time processes

In this work, we propose estimators for the variance of mean residual times, which rely on individual residence times. The latter are assumed to be described by independent and identically distributed random variables, generated by a discrete-time stochastic process. We examine their performance through numerical experiments involving well-known probability distributions, and an application example using molecular dynamics simulation results, from an aqueous NaCl solution, is provided. These computationally inexpensive estimators, capable of achieving very accurate outcomes, serve as useful tools for assessing and reporting uncertainties in mean residual times across a wide range of simulations.

“THE HANDMAID’S TALE” BY MARGARET ATWOOD AS A POSTMODERN NOVEL: DYSTOPIAN GENRE TRANSGRESSION IN POSTMODERN ERA

Margaret Atwood’s novel “The Handmaid’s Tale” seems to have been studied comprehensively and fundamentally. Aspects of the dystopian genre, its feminist and anti-religious orientation, and the novel’s connection with philosophical concepts of the 20th century have been studied in depth. In the poetics of the novel, researchers’ interest in the problems of intertextuality, the specifics of composition, etc., has never ceased. However, despite the variety of problems covered in these studies, in our opinion, a fundamental question about the significance of Margaret Atwood’s novel for the further development of the tradition of the dystopian genre has remained on the periphery of scholarly attention. Meanwhile, “The Handmaid’s Tale” can be regarded as a programmatic work that clearly identifies and elaborates the key genre principles of the postmodern dystopian novel, which have not yet been substantiated. Modern studies of the features of postmodern dystopia based on the material of various works of the 1990-2000s, as well as in modern findings, capture exactly those genre strategies that were embedded in M. Atwood’s novel. At the same time, researchers focus on the transformation of the mainly predominant aspects of dystopia in the era of postmodernism. Meanwhile, the changes that dystopia underwent in the last third of the 20th century are associated with the formation of the aesthetics of the genre of the postmodern novel, as evidenced by the publication of the novel “The Handmaid’s Tale”. In this regard, we consider it appropriate to study M. Atwood’s novel as a postmodern dystopian novel in the relationship between the content features of dystopia and the genre of the postmodern novel. The work aims to investigate the dystopian narrative presented in “The Handmaid’s Tale” in the context of the poetics of the postmodern novel genre. Achieving the stated goal involves the use of historicalliterary, philosophical-aesthetic, and hermeneutical research methods. In the context of the postmodern dystopian paradigm, the genre of dystopia is transformed significantly. Changes in the substantive aspects of the genre are associated with a reduction in the gap between dystopian and real time, the affirmation of a relatively optimistic tone, the lability of the dystopian world (which predetermines the conditionally metaphorical nature of the chronotope, the amorphousness of spatial and discrete time boundaries), and a shift in emphasis to the inner world of the character. The increased degree of anthropocentrism, which is characteristic of postmodern dystopia, determines the change in the nature of the protagonist’s rebellion against the totalitarian regime – the focus of social rebellion shifts to personal existential (the struggle to preserve one’s own identity), where it is not the result that is important, but its philosophical content. At the same time, dystopia also absorbs the features of the postmodern novel form and postmodern narrative strategy, mastering the techniques of intertextuality and rethinking the traditions of the past, irony and parody, playing with time and the author’s game with the reader. Moreover, the function of the author’s game strategy is not only to make the reader a co-author of the text but also to encourage him to make multiple interpretations. The multifaceted nature of the game draws the reader into the action and forces one to reflect on the windows of opportunity opening up in modern civilization, that is, to perceive the story of Gilead as more than just exciting storytelling. The game mode reveals the author’s ideological and content-based storytelling strategy – through intertext (as a combination of multi-level chronotopes and cultural texts), on the one hand, and through involvement in the experiences of Offred, on the other, to encourage/force the reader to experience the entire history of Christian civilization, presented in the dystopian heroine’s narrative.

Effect of mental health staffing inputs on initiation of care among recently separated Veterans.

To estimate a causal relationship between mental health staffing and time to initiation of mental health care for new patients. As the largest integrated health care delivery system in the United States, the Veterans Health Administration (VHA) provides a unique setting for isolating the effects of staffing on initiation of mental health care where demand is high and out-of-pocket costs are not a relevant confounder. We use data from the Department of Defense and VHA to obtain patient and facility characteristics and health care use. To isolate exogenous variation in mental health staffing, we used an instrumental variables approach-two-stage residual inclusion with a discrete time hazard model. Our outcome is time to initiation of mental health care after separation from active duty (first appointment) and our exposure is mental health staffing (standardized clinic time per 1000 VHA enrollees per pay period). Our cohort consists of all Veterans separating from active duty between July 2014 and September 2017, who were enrolled in the VHA, and had at least one diagnosis of post-traumatic stress disorder, major depressive disorder, and/or substance use disorder in the year prior to separation from active duty (N = 54,209). An increase of 1 standard deviation in mental health staffing results in a higher likelihood of initiating mental health care (adjusted hazard ratio: 3.17, 95% confidence interval: 2.62, 3.84, p < 0.001). Models stratified by tertile of mental health staffing exhibit decreasing returns to scale. Increases in mental health staffing led to faster initiation of care and are especially beneficial in facilities where staffing is lower, although initiation of care appears capacity-limited everywhere.

Linear, Nonlinear, and Distributed-Parameter Observers Used for (Renewable) Energy Processes and Systems—An Overview

Full- and reduced-order observers have been used in many engineering applications, particularly for energy systems. Applications of observers to energy systems are twofold: (1) the use of observed variables of dynamic systems for the purpose of feedback control and (2) the use of observers in their own right to observe (estimate) state variables of particular energy processes and systems. In addition to the classical Luenberger-type observers, we will review some papers on functional, fractional, and disturbance observers, as well as sliding-mode observers used for energy systems. Observers have been applied to energy systems in both continuous and discrete time domains and in both deterministic and stochastic problem formulations to observe (estimate) state variables over either finite or infinite time (steady-state) intervals. This overview paper will provide a detailed overview of observers used for linear and linearized mathematical models of energy systems and review the most important and most recent papers on the use of observers for nonlinear lumped (concentrated)-parameter systems. The emphasis will be on applications of observers to renewable energy systems, such as fuel cells, batteries, solar cells, and wind turbines. In addition, we will present recent research results on the use of observers for distributed-parameter systems and comment on their actual and potential applications in energy processes and systems. Due to the large number of papers that have been published on this topic, we will concentrate our attention mostly on papers published in high-quality journals in recent years, mostly in the past decade.

Numerical Solution of Heat Equation using Modified Cubic B-spline Collocation Method

In this paper, a collocation method is presented based on the Modified Cubic B-spline Method (MCBSM) for the numerical solution of the heat equation. The PDE is fully discretized by using the Modified Cubic B-spline basis collocation for spatial discretization and the finite difference method is used for the time discretization. A numerical example from PDE is used to evaluate the accuracy of the proposed method. The numerical results are evaluated in comparison to the exact solutions. The findings consistently indicate that the suggested technique provides good error estimates. We also discovered that our proposed method was unconditionally stable. Hence, based on the results and the efficiency of the method, the method is suitable for solving heat equation.

On the BEM solution of convection–diffusion type equations involving variable convective coefficients

In this study, numerical solutions of the unsteady convection–diffusion type equations of variable convective coefficients are investigated by two effective techniques alternative to direct boundary element method (BEM). That is, the domain boundary element and the dual reciprocity BEMs with the fundamental solution of convection–diffusion equation are used in space to transform the governing differential equations into equivalent integral equations while a backward finite difference scheme is utilized in time discretization. The fruitfulness of these combined techniques are shown by the implementation of the techniques for some widely investigated fluid dynamics problems. In fact, the lid-driven cavity flow is solved, and precise results are attained as benchmarks for assessing the accuracy of the aforementioned methods. Further, the application of the methods is extended for the natural convection flow which is governed mainly by the convection–diffusion type equations accompanied by the velocity components as variable convective coefficients. The obtained numerical results reveal that the domain BEM which uses the fundamental solution of convection–diffusion equation captures the characteristics and physical advancement of the fluid flow quite well at various combined values of the problem physical parameters.