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Journal articles on the topic 'BDF method'

Author: Grafiati

Published: 4 June 2025

Last updated: 1 August 2025

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1

Zhang, Chenyu, Xiaodong Du, Songhan Zeng, et al. "Photolytic Formation of Polybrominated Dibenzofurans (PBDFs) in Various Simulated Soil-Washing Solutions Containing Polybrominated Diphenyl Ethers (PBDEs)." Processes 13, no. 6 (2025): 1806. https://doi.org/10.3390/pr13061806.

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Soil washing is an efficient method to remove polybrominated diphenyl ethers (PBDEs) from contaminated soils. The obtained solutions from soil-washing still contain PBDEs, requiring further treatment before disposal or reuse. Although photolysis is effective for PBDE degradation in solutions, the concurrent formation of toxic polybrominated dibenzofurans (PBDFs) may limit its practical application. In this study, 2,8-dibromodibenzofurans (2,8-BDF) formation rate and mechanisms during 2,4,4′-tribromodiphenyl ether (BDE-28) photolysis in various simulated soil-washing solutions was investigated.

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Mariame, Cissé, Assoumou Ebah Carine, Kouadio Natia Joseph, Kra Kouassi A. Séverin, and Niamké Sébastien. "Nutritional Evaluation and Sensory Description of Five Porridges Formulated from Certain Local Commodities for Use as Supplementary Foods for Children in Côte d’Ivoire." Scholars Academic Journal of Biosciences 12, no. 10 (2024): 358–65. http://dx.doi.org/10.36347/sajb.2024.v12i10.005.

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The aim of this work was to evaluate the nutritional, vitamin and sensory potential of porridges for infant feeding. Endeed, malnutrition in weaning infants and young children is a major public health and social problem in developing countries. It is therefore essential to develop appropriate complementary food formulations to address this problem. In this context, different flours have been developed from local raw materials (cereals and pulses) in combination with other ingredients. Five porridges, B1F, B2F, B3F, B4F and B5F were prepared from five flours formulated with several ingredients

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Fook, Tiaw Kah, and Zarina Bibi Ibrahim. "Block Backward Differentiation Formulas for solving second order Fuzzy Differential Equations." MATEMATIKA 33, no. 2 (2017): 215. http://dx.doi.org/10.11113/matematika.v33.n2.868.

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In this paper, we study the numerical method for solving second order Fuzzy Differential Equations (FDEs) using Block Backward Differential Formulas (BBDF) under generalized concept of higher-order fuzzy differentiability. Implementation of the method using Newton iteration is discussed. Numerical results obtained by BBDF are presented and compared with Backward Differential Formulas (BDF) and exact solutions. Several numerical examples are provided to illustrate our methods.

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Le, Hanh Ngoc Thi, Kiyoshi Imamura, Masakazu Furuta, Luu Van Boi, and Yasuaki Maeda. "Production of biodiesel from Vernicia montana Lour. oil using a co-solvent method and the subsequent evaluation of its stability during storage." Green Processing and Synthesis 7, no. 2 (2018): 170–79. http://dx.doi.org/10.1515/gps-2016-0215.

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AbstractThe costs associated with the production of biodiesel fuel (BDF) are directly affected by the nature of the feedstock material and the methods used during the production process. In Southeast Asia, many non-edible oils are used to produce BDFs, as exemplified by the recent use of the non-edible oil derived fromVernicia montanaLour. in Laos and Vietnam for the production of BDF. In this work, we developed an improved procedure for the production of BDF fromVernicia montanaoil consisting of 80.3%±0.5% α-eleostearic acid moiety (C18:3) using a co-solvent method. Furthermore, the stability

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Prianka, Dian. "Evaluating the Impact of Basic Design Fundamentals Education on the Creative Process of Fashion Design Students in Surabaya, Indonesia." Humanities & Language: International Journal of Linguistics, Humanities, and Education 1, no. 1 (2023): 15–21. http://dx.doi.org/10.32734/qxkg8a61.

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This academic paper explores the influence of Basic Design Fundamentals (BDF) education on the creative process of fashion design students in Surabaya, Indonesia. BDF education, rooted in the principles of design, serves as a foundational element in various design disciplines, including fashion. The study employs a mixed-method research approach, combining quantitative Likert scale assessments and qualitative interviews with ten students from the University of Surabaya's fashion design program. The research reveals that BDF education significantly enhances the creative abilities of fashion des

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Ryanividya, Dunyafanisa Nurul Aulia, Ahmad Alamsyah, and Siska Cicilia. "Mutu Kue Bingka Dolu pada Berbagai Konsentrasi Substitusi Terigu dengan Tepung Sorgum." Pro Food 8, no. 2 (2022): 107–15. http://dx.doi.org/10.29303/profood.v8i2.273.

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Bingka dolu is a traditional snack from Bima, West Nusa Tenggara. They are much favored by the community because because of the unique taste and flavor. This study aims to determine the percentage of the use of the best sorghum flour as a substitute for flour on the quality of bingka dolu. This research method was CRD with one factor, namely the percentage of substitution of flour with sorghum flour (BD), namely BD0 (100%: 0%); BD1 (80% : 20%); BD2 (605 : 40%); BD3(40% : 60%); BD4 (20% : 80%) and BD5 (0% : 100%) with parameters such as moisture content, ash, crude fiber, taste, aroma, and text

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Suehara, Ken-Ichiro, Kazuo Owari, Jiro Kohda, Yasuhisa Nakano, and Takuo Yano. "Rapid and Simple Determination of Oil and Urea Concentrations and Solids Content to Monitor Biodegradation Conditions of Wastewater Discharged from a Biodiesel Fuel Production Plant." Journal of Near Infrared Spectroscopy 15, no. 2 (2007): 89–96. http://dx.doi.org/10.1255/jnirs.721.

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To prepare and maintain the optimal biodegradation conditions of wastewater discharged from a biodiesel fuel (BDF) production process with alkali–catalysis transesterification, rapid and simple methods were investigated to measure oil (carbon source of microorganisms) and urea (nitrogen source) concentrations and solids content (indicator of growth inhibition of microorganism) of the wastewater. Two non-destructive methods were investigated. First, physical properties of the BDF wastewater such as electric conductivity (EC), specific gravity (Sp.Gr.) and Brix values were measured and the value

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8

Momoniat, E., C. Harley, and M. Berman. "On the Use of Backward Difference Formulae to Improve the Prediction of Direction in Market Related Data." Mathematical Problems in Engineering 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/652653.

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The use of a BDF method as a tool to correct the direction of predictions made using curve fitting techniques is investigated. Random data is generated in such a fashion that it has the same properties as the data we are modelling. The data is assumed to have “memory” such that certain information imbedded in the data will remain within a certain range of points. Data within this period where “memory” exists—say at time stepst1,t2,…,tn—is curve-fitted to produce a prediction at the next discrete time step,tn+1. In this manner a vector of predictions is generated and converted into a discrete o

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Baleanu, Dumitru, Mohammad Mehdizadeh Khalsaraei, Ali Shokri, and Kamal Kaveh. "On the boundedness stepsizes-coefficients of A-BDF methods." AIMS Mathematics 7, no. 2 (2022): 1562–79. http://dx.doi.org/10.3934/math.2022091.

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<abstract><p>Physical constraints must be taken into account in solving partial differential equations (PDEs) in modeling physical phenomenon time evolution of chemical or biological species. In other words, numerical schemes ought to be devised in a way that numerical results may have the same qualitative properties as those of the theoretical results. Methods with monotonicity preserving property possess a qualitative feature that renders them practically proper for solving hyperbolic systems. The need for monotonicity signifies the essential boundedness properties necessary for

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10

Stewart, Jared, Mayya Tokman, Valentin Dallerit, Fabrizio Bisetti, and Oscar Diaz-Ibarra. "Variable Time-stepping Exponential Integrators for Chemical Reactors with Analytical Jacobians." Applied and Computational Mathematics 13, no. 2 (2024): 29–37. http://dx.doi.org/10.11648/j.acm.20241302.11.

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Chemical combustion problems are known to be stiff and therefore difficult to efficiently integrate in time when numerically simulated. Implicit methods, such as backwards differentiation formula (BDF), are widely considered to be the state-of-the-art methods owing their capability of taking relatively large time-steps while maintaining accurate combustion characteristics. Exponential time integration methods have recently demonstrated the ability to accurately and efficiently solve large scale systems of ordinary differential equations. This study introduces a novel adaptive time stepping exp

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Intentilia, Anak Agung Mia. "The Trajectory of Bali Democracy Forum: Indonesia’s Soft Power and Nation Branding." Politicos: Jurnal Politik Dan Pemerintahan 5, no. 1 (2025): 45–56. https://doi.org/10.22225/politicos.5.1.2025.45-56.

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As one of the largest Muslim-majority countries with an emerging economy, the conversation regarding Indonesia’s democracy has always been intriguing. The path of Indonesia’s democratic values has evolved from Independence Day to the current globalization era. In addition to examining Indonesia’s domestic reforms, the contemporary issues of this country’s role in shaping the regional architecture of democracy have also expanded to the realm of international relations. In 2008, Indonesia initiated the Bali Democracy Forum (BDF) as an annual platform to promote dialogue-based cooperation and uph

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Zwarycz-Makles, Katarzyna, and Dorota Majorkowska-Mech. "Gear and Runge–Kutta Numerical Discretization Methods in Differential Equations of Adsorption in Adsorption Heat Pump." Applied Sciences 8, no. 12 (2018): 2437. http://dx.doi.org/10.3390/app8122437.

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The main aim of this paper was to find the correct method of calculating equations of heat and mass transfer for the adsorption process and to calculate it numerically in reasonable time and with proper accuracy. An adsorption heat pump with a silica gel adsorbent and water adsorbate is discussed. We developed a mathematical model of temperature and uptake changes in the adsorber/desorber comprising the set of heat and mass balance partial differential equations (PDEs), together with the initial and boundary conditions and solved it by the numerical method of lines (NMOL). Spatial discretizati

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Alberdi Celaya, Elisabete, та Juan Jose Anza. "BDF-α : A Multistep Method with Numerical Damping Control". Universal Journal of Computational Mathematics 1, № 3 (2013): 96–108. http://dx.doi.org/10.13189/ujcmj.2013.010305.

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14

Akrivis, Georgios, Minghua Chen, Fan Yu, and Zhi Zhou. "The Energy Technique for the Six-Step BDF Method." SIAM Journal on Numerical Analysis 59, no. 5 (2021): 2449–72. http://dx.doi.org/10.1137/21m1392656.

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15

Zhu, Ning, and Kuo Ming-chi. "BDF Synthesis based on Environment-friendly Ultrasound Irradiation Method." Proceedings of the Thermal Engineering Conference 2018 (2018): 0201. http://dx.doi.org/10.1299/jsmeted.2018.0201.

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16

RONIZAM, NUR FARAH NAJIHA, SITI AINOR MOHD YATIM, and ISKANDAR SHAH MOHD ZAWAWI. "THE PREDICTOR-CORRECTOR BACKWARD DIFFERENCE FORMULAS TO ESTIMATE THE TREND OF RIVER WATER QUALITY." JOURNAL OF SUSTAINABILITY SCIENCE AND MANAGEMENT 19, no. 8 (2024): 103–15. http://dx.doi.org/10.46754/jssm.2024.08.008.

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The time-series trend analysis is a mathematical technique that attempts to estimate future data movement based on observed previous and current data. This can include analysing long-terms changes in river water quality in order to emphasise river management in the future. Therefore, in this study, the backward difference formula (BDF) with forward and central difference approximations is derived to estimate a of 20-year trend in water quality index (WQI) data at the Selangor River basin in Malaysia. As an adaptation of the conventional BDF and predictor-corrector scheme, the Euler’s method wi

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17

Zhou, Yunyi, Ziyi Feng, Chunling Chen, and Fenghua Yu. "Bilinear Distance Feature Network for Semantic Segmentation in PowerLine Corridor Point Clouds." Sensors 24, no. 15 (2024): 5021. http://dx.doi.org/10.3390/s24155021.

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Semantic segmentation of target objects in power transmission line corridor point cloud scenes is a crucial step in powerline tree barrier detection. The massive quantity, disordered distribution, and non-uniformity of point clouds in power transmission line corridor scenes pose significant challenges for feature extraction. Previous studies have often overlooked the core utilization of spatial information, limiting the network’s ability to understand complex geometric shapes. To overcome this limitation, this paper focuses on enhancing the deep expression of spatial geometric information in s

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18

Hernández, Vicente, Jacinto Javier Ibáñez, Jesús Peinado, and Enrique Arias. "A GMRES-based BDF method for solving differential Riccati equations." Applied Mathematics and Computation 196, no. 2 (2008): 613–26. http://dx.doi.org/10.1016/j.amc.2007.06.021.

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19

Yahaya, Muritala, Abdulkadir Abubakar, and Yusuf Dauda Jikantoro. "DEVELOPMENT OF A CONTINUOUS BACKWARD DIFFERENTIATION FORMULAE FOR SOLVING FIRST-ORDER AND SECOND-ORDER INITIAL VALUE PROBLEM." FUDMA JOURNAL OF SCIENCES 9, no. 5 (2025): 14–22. https://doi.org/10.33003/fjs-2025-0905-3633.

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Numerical methods for solving ordinary differential equations (ODEs) are essential in modeling dynamical systems across science and engineering. While specialized methods exist for first-order and second-order ODEs, developing a unified approach that efficiently handles both classes remain an active area of research. In this paper, we present a novel two-step hybrid block method based on the backward differentiation formula (BDF), capable of approximating solutions for both first- and second-order ODEs without requiring separate derivations. The method is constructed using interpolation and co

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20

Liu, X., M. H. Song, and M. Z. Liu. "Linear Multistep Methods for Impulsive Differential Equations." Discrete Dynamics in Nature and Society 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/652928.

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This paper deals with the convergence and stability of linear multistep methods for impulsive differential equations. Numerical experiments demonstrate that both the mid-point rule and two-step BDF method are of orderp=0when applied to impulsive differential equations. An improved linear multistep method is proposed. Convergence and stability conditions of the improved methods are given in the paper. Numerical experiments are given in the end to illustrate the conclusion.

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21

Tong, T. O., M. C. Kekana, M. Y. Shatalov, and S. P. Moshokoa. "Accuracy Tests on Built-In Algorithms Applied to the Lorenz System." Journal of Computational and Theoretical Nanoscience 16, no. 10 (2019): 4064–71. http://dx.doi.org/10.1166/jctn.2019.8486.

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This work investigate, An idea of checking accuracy of algorithms from mathematical black box by means of residual functions. Lorenz system is used as case study as the chaotic system does not have analytical solution. The numerical procedures examined include BDF, Adams method and Implicit Runge Kutta methods. The interval of numerical results is t ∈ [0; 10].

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22

Longé, Lionel F., Laurent Michely, Antoine Gallos, et al. "Improved Processability and Antioxidant Behavior of Poly(3-hydroxybutyrate) in Presence of Ferulic Acid-Based Additives." Bioengineering 9, no. 3 (2022): 100. http://dx.doi.org/10.3390/bioengineering9030100.

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Poly(3-hydroxybutyrate), PHB, has gathered a lot of attention for its promising properties—in particular its biobased nature and high biodegradability. Although PHB is prime candidate for the packaging industry, the applications are still limited by a narrow processing window and thermal degradation during melt processing. In this work, three novel additives based on ferulic acid esterified with butanediol, pentanediol, and glycerol (BDF, PDF, and GTF, respectively) were used as plasticizers and antioxidative additives to improve mechanical properties of PHB. Elongation at break up to 270% was

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23

Lou, Yimin, and Christoph Lehrenfeld. "Isoparametric Unfitted BDF--Finite Element Method for PDEs on Evolving Domains." SIAM Journal on Numerical Analysis 60, no. 4 (2022): 2069–98. http://dx.doi.org/10.1137/21m142126x.

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24

Arias, Enrique, Vicente Hernández, Jacinto Javier Ibáñez, and Jesús Peinado. "A fixed point-based BDF method for solving differential Riccati equations." Applied Mathematics and Computation 188, no. 2 (2007): 1319–33. http://dx.doi.org/10.1016/j.amc.2006.11.001.

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25

Yatim, S. A. M., Z. B. Ibrahim, K. I. Othman, and M. B. Suleiman. "A Quantitative Comparison of Numerical Method for Solving Stiff Ordinary Differential Equations." Mathematical Problems in Engineering 2011 (2011): 1–12. http://dx.doi.org/10.1155/2011/193691.

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We derive a variable step of the implicit block methods based on the backward differentiation formulae (BDF) for solving stiff initial value problems (IVPs). A simplified strategy in controlling the step size is proposed with the aim of optimizing the performance in terms of precision and computation time. The numerical results obtained support the enhancement of the method proposed as compared to MATLAB's suite of ordinary differential equations (ODEs) solvers, namely, ode15s and ode23s.

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Lang, Jens, and Bernhard A. Schmitt. "Implicit A-Stable Peer Triplets for ODE Constrained Optimal Control Problems." Algorithms 15, no. 9 (2022): 310. http://dx.doi.org/10.3390/a15090310.

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This paper is concerned with the construction and convergence analysis of novel implicit Peer triplets of two-step nature with four stages for nonlinear ODE constrained optimal control problems. We combine the property of superconvergence of some standard Peer method for inner grid points with carefully designed starting and end methods to achieve order four for the state variables and order three for the adjoint variables in a first-discretize-then-optimize approach together with A-stability. The notion triplets emphasize that these three different Peer methods have to satisfy additional matc

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27

Asnor, Mohd Yatim, and Ibrahim. "Solving Directly Higher Order Ordinary Differential Equations by Using Variable Order Block Backward Differentiation Formulae." Symmetry 11, no. 10 (2019): 1289. http://dx.doi.org/10.3390/sym11101289.

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Variable order block backward differentiation formulae (VOHOBBDF) method is employedfor treating numerically higher order Ordinary Differential Equations (ODEs). In this respect, the purpose of this research is to treat initial value problem (IVP) of higher order stiff ODEs directly. BBDF method is symmetrical to BDF method but it has the advantage of producing more than one solutions simultaneously. Order three, four, and five of VOHOBBDF are developed and implemented as a single code by applying adaptive order approach to enhance the computational efficiency. This approach enables the select

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28

Ramos, Higinio, and Jesús Vigo-Aguiar. "A fourth-order Runge–Kutta method based on BDF-type Chebyshev approximations." Journal of Computational and Applied Mathematics 204, no. 1 (2007): 124–36. http://dx.doi.org/10.1016/j.cam.2006.04.033.

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29

Tokić, Amir, Ivo Uglešić, and Gorazd Štumberger. "Simulations of Transformer Inrush Current by Using BDF-Based Numerical Methods." Mathematical Problems in Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/215647.

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This paper describes three different ways of transformer modeling for inrush current simulations. The developed transformer models are not dependent on an integration step, thus they can be incorporated in a state-space form of stiff differential equation systems. The eigenvalue propagations during simulation time cause very stiff equation systems. The state-space equation systems are solved by usingA- andL-stable numerical differentiation formulas (NDF2) method. This method suppresses spurious numerical oscillations in the transient simulations. The comparisons between measured and simulated

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Alhassan, Buhari, Hamza Yusuf, and Abdulrahman Adamu. "Analysis of Convergence and Stability Properties of Diagonally Implicit 3-Point Block Backward Differentiation Formula for First Order Stiff Initial Value Problems." UMYU Scientifica 3, no. 2 (2024): 186–201. http://dx.doi.org/10.56919/usci.2432.021.

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Study’s Excerpt/Novelty This paper introduces a novel diagonally implicit 3-point block backward differentiation formula (BDF) for efficiently solving first-order stiff initial value problems. The method, proven to have an order of accuracy of 5, meets the necessary and sufficient conditions for convergence, including consistency and zero stability. Comparative numerical results highlight its superior performance in terms of maximum error and CPU time, demonstrating its advantage over existing methods and offering a robust solution for integrating stiff initial value problems. Full Abstract Th

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31

Kaze, Atsi, Adiku Lydia, Yarima Namuma, and G. M. Kumleng. "A Second Derivative Block Method Derived from a Family of Modified Backward Differentiation Formula (BDF) Type for Solving Stiff Ordinary Differential Equations." i-manager’s Journal on Mathematics 11, no. 2 (2022): 8. http://dx.doi.org/10.26634/jmat.11.2.19206.

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In this work, a second derivative block method derived from a family of modified backward differentiation formula (bdf) type for solving stiff ordinary differential equations has been constructed. Choosing a step number, k = 4, four discrete methods with uniform order 7 are obtained using the multistep collocation approach. The stability properties of the new method have been established. The solutions of two problems have been computed and compared with the corresponding exact and other existing solutions. Solutions are presented on graphs and the associated absolute errors are compared in ta

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32

Castelo, Antonio, Geovan Tavares, and Juliana Bertoco. "Numerical solutions for implicit differential equations with singularities." Semina: Ciências Exatas e Tecnológicas 43, no. 1Esp (2022): 3. http://dx.doi.org/10.5433/1679-0375.2022v43n1espp3.

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In this paper we introduce a technique to deal with implicit differential equations exhibiting singularities. Our approach is a geometrical one, we use the concept of contact structure on a manifold associated with the differential equation. In this setting we prove an existence and uniqueness theorem. We also show how it relates to known geometric results for this kind of equation. We also indicate how the method can be implemented by using continuation methods techniques and the BDF (Backward Differentiation Formula).

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Kekana, M. C., M. Y. Shatalov, T. O. Tong, and S. E. Fadugba. "ANALYSIS OF R¨OSSLER ATTRACTOR BY MEANS OF RESIDUAL AND JOUBERT-GREEFF METHODS." South East Asian Journal of Mathematics and Mathematical Sciences 19, no. 02 (2023): 431–50. http://dx.doi.org/10.56827/seajmms.2023.1902.32.

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In this paper, A mathematical framework of checking accuracy of numericalmethods from mathematical software is been developed and investigated.R¨ossler attractor is used as case study as its analytical solution is non-existence.The algorithms investigated from Mathcad software includes AdamsBDF, Adams,BDF and Runge-Kutta fixed methods. The numerical solutions of each built-inalgorithms are compared to well-known Joubert-Greeff method. The estimationof global and local residuals are shown. The graphical results are plotted on aninterval of 0 ≤ t ≤ 150.

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Abasi, Naghmeh, Mohamed Suleiman, Neda Abbasi, and Hamisu Musa. "2-Point Block BDF Method with Off-Step Points for Solving Stiff ODEs." Journal of Soft Computing and Applications 2014 (2014): 1–15. http://dx.doi.org/10.5899/2014/jsca-00039.

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Wang, Junjun, and Xiaoxia Yang. "Superconvergence analysis for a nonlinear parabolic equation with a BDF finite element method." International Journal of Computer Mathematics 97, no. 12 (2020): 2487–506. http://dx.doi.org/10.1080/00207160.2019.1706729.

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Vardcharragosad, Pichit, Luis F. Ayala, and Miao Zhang. "Linear vs. Radial Boundary-Dominated Flow: Implications for Gas-Well-Decline Analysis." SPE Journal 20, no. 05 (2015): 1053–66. http://dx.doi.org/10.2118/176020-pa.

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Summary Linear flow is a fundamental reservoir-flow geometry typically associated with production from unconventional resources stimulated by means of hydraulic fracturing. Recently, linear flow has been intensively studied following the fast pace of development of unconventional resources. Previous studies have mainly focused on early transient behavior and behavior of composite linear-flow systems. In this work, a density-based analysis method is extended to study decline behavior of the linear-flow system in boundary-dominated flow (BDF). In this study, we first discuss traditional approach

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Sadek, Lakhlifa, El Mostafa Sadek, and Hamad Talibi Alaoui. "On Some Numerical Methods for Solving Large Differential Nonsymmetric Stein Matrix Equations." Mathematical and Computational Applications 27, no. 4 (2022): 69. http://dx.doi.org/10.3390/mca27040069.

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In this paper, we propose a new numerical method based on the extended block Arnoldi algorithm for solving large-scale differential nonsymmetric Stein matrix equations with low-rank right-hand sides. This algorithm is based on projecting the initial problem on the extended block Krylov subspace to obtain a low-dimensional differential Stein matrix equation. The obtained reduced-order problem is solved by the backward differentiation formula (BDF) method or the Rosenbrock (Ros) method, the obtained solution is used to build the low-rank approximate solution of the original problem. We give some

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Ducinskas, Kestutis, and Lina Dreiziene. "Performance Evaluations of Gaussian Spatial Data Classifiers Based on Hybrid Actual Error Rate Estimators." Austrian Journal of Statistics 49, no. 4 (2020): 27–34. http://dx.doi.org/10.17713/ajs.v49i4.1122.

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Discrimination and classification of spatial data has been widely mentioned in the scientific literature, but lacks full mathematical treatment and easily available algorithms and software. This paper fills this gap by introducing the method of statistical classification based on Bayes discriminant function (BDF) and by providing original approach for the classifier performance evaluation. Supervised classification of spatial data with response variable modelled by Gaussian random fields (GRF) with continuous or discrete spatial index is studied. Populations are assumed to be with different re

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Zhao, Yanzi, and Xinlong Feng. "Solving the Incompressible Surface Stokes Equation by Standard Velocity-Correction Projection Methods." Entropy 24, no. 10 (2022): 1338. http://dx.doi.org/10.3390/e24101338.

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In this paper, an effective numerical algorithm for the Stokes equation of a curved surface is presented and analyzed. The velocity field was decoupled from the pressure by the standard velocity correction projection method, and the penalty term was introduced to make the velocity satisfy the tangential condition. The first-order backward Euler scheme and second-order BDF scheme are used to discretize the time separately, and the stability of the two schemes is analyzed. The mixed finite element pair (P2,P1) is applied to discretization of space. Finally, numerical examples are given to verify

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Zhang, Haixiang, and Xuehua Yang. "The BDF orthogonal spline collocation method for the two-dimensional evolution equation with memory." International Journal of Computer Mathematics 95, no. 10 (2017): 2011–25. http://dx.doi.org/10.1080/00207160.2017.1347259.

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Sadek, L., and H. Talibi Alaoui. "The extended nonsymmetric block Lanczos methods for solving large-scale differential Lyapunov equations." Mathematical Modeling and Computing 8, no. 3 (2021): 526–36. http://dx.doi.org/10.23939/mmc2021.03.526.

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In this paper, we present a new approach for solving large-scale differential Lyapunov equations. The proposed approach is based on projection of the initial problem onto an extended block Krylov subspace by using extended nonsymmetric block Lanczos algorithm then, we get a low-dimensional differential Lyapunov matrix equation. The latter differential matrix equation is solved by the Backward Differentiation Formula method (BDF) or Rosenbrock method (ROS), the obtained solution allows to build a low-rank approximate solution of the original problem. Moreover, we also give some theoretical resu

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Sorokin, Vsevolod G., and Andrei V. Vyazmin. "Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration." Mathematics 10, no. 11 (2022): 1886. http://dx.doi.org/10.3390/math10111886.

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The paper describes essential reaction–diffusion models with delay arising in population theory, medicine, epidemiology, biology, chemistry, control theory, and the mathematical theory of artificial neural networks. A review of publications on the exact solutions and methods for their construction is carried out. Basic numerical methods for integrating nonlinear reaction–diffusion equations with delay are considered. The focus is on the method of lines. This method is based on the approximation of spatial derivatives by the corresponding finite differences, as a result of which the original de

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Zhang, Lixia, Hao Jiang, Yong Li, Xinmin Song, and Yang Li. "An Explicit Method for Estimating the Average Reservoir Pressure and Gas in Place Based on the Gas Property Polynomial Function." Geofluids 2023 (January 30, 2023): 1–21. http://dx.doi.org/10.1155/2023/4003656.

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The fast and accurate determination of average reservoir pressure (ARP) and gas reserves is vital for the analysis and forecasting of gas well performance. An explicit and relatively rigorous method for estimating the ARP and gas in place, based on the dynamic material balance equation and the gas property polynomial function (GPPF), is presented to circumvent such drawbacks as high cost, empiricism, poor adaptability to variable production schedules, and the necessity for iteration processes, by which current approaches usually have been limited. The gas flow model is solved by introducing ps

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Tong, T. O., M. C. Kekana, M. Y. Shatalov, and S. P. Moshokoa. "Numerical Investigation of Brusselator Chemical Model by Residual Function Using Mathematica Software." Journal of Computational and Theoretical Nanoscience 17, no. 7 (2020): 2947–54. http://dx.doi.org/10.1166/jctn.2020.9324.

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In recent years, mathematical models have been developed to illustrate some physical phenomena in science and engineering. One of those systems of nonlinear differential equations is Brusselator chemical model. A mathematical template of checking accuracy of from black-boxes has been developed and investigated. Brusselator model is used as case study as its analytical solution is non-existence. The algorithms investigated from Mathematica software includes Adams method, Backward differential formula (BDF) and Implicit Runge-Kutta method which works well on stiff systems. The graphical results

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Rezaee, Vahid, and Arash Houshmand. "NUMERICAL SOLUTION OF NON-SIMILAR BOUNDARY-LAYER FLOW OVER A CYLINDER." Journal of the Serbian Society for Computational Mechanics 17, no. 1 (2023): 134–50. http://dx.doi.org/10.24874/jsscm.2023.17.01.10.

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This paper presents Ð° numerical solution of a non-similar two-dimensional boundary-layer flow over a cylinder. The assumptions and related two-dimensional flow equations are presented. The fourth-order Runge-Kutta method with the backward differentiation formula (BDF) method to separation point is implemented in the numerical solution using MATLAB software. Numerical solution results are compared with well-known analytic solutions. Shear stress diagram, friction ratio based on Î¸ and x, and output results are illustrated. The results of numerical solution demonstrate good consistency with ana

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Dao, Tu Van, Chu Van Nguyen, Quang Tien Nguyen, et al. "Evaluation of Tumor Budding in Predicting Survival for Gastric Carcinoma Patients in Vietnam." Cancer Control 27, no. 1 (2020): 107327482096888. http://dx.doi.org/10.1177/1073274820968883.

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Background: Tumor budding (Bd) has been demonstrated to be a promising prognostic factor in many carcinomas and in gastric cancer. It may represent an optimal additional parameter that is helpful for risk stratification in gastric adenocarcinoma. Hence, the present research was designed to predict the survival outcomes of gastric cancer in Vietnam, applying the tumor budding criteria of the International Tumor Budding Consensus Conference (ITBCC) 2016. Methods: The present study was conducted on 109 gastric cancer patients who underwent surgery but did not receive neo-adjuvant chemotherapy fro

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Minghua Chen, Minghua Chen, Fan Yu Fan Yu, and Qingdong Zhang Qingdong Zhang. "The Weighted and Shifted Two-Step BDF Method for Allen-Cahn Equation on Variable Grids." International Journal of Numerical Analysis and Modeling 22, no. 5 (2025): 671–93. https://doi.org/10.4208/ijnam2025-1029.

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Pimenov, V. G., and A. S. Hendy. "Numerical Studies for Fractional Functional Differential Equations with Delay Based on BDF-Type Shifted Chebyshev Approximations." Abstract and Applied Analysis 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/510875.

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Fractional functional differential equations with delay (FDDEs) have recently played a significant role in modeling of many real areas of sciences such as physics, engineering, biology, medicine, and economics. FDDEs often cannot be solved analytically so the approximate and numerical methods should be adapted to solve these types of equations. In this paper we consider a new method of backward differentiation formula- (BDF-) type for solving FDDEs. This approach is based on the interval approximation of the true solution using the Clenshaw and Curtis formula that is based on the truncated shi

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Uddin, Rahim, Jianxiang Wen, Tao He, Fufei Pang, Zhenyi Chen, and Tingyun Wang. "Ultraviolet Irradiation Effects on luminescent Centres in Bismuth-Doped and Bismuth-Erbium Co-Doped Optical Fibers via Atomic Layer Deposition." Electronics 7, no. 10 (2018): 259. http://dx.doi.org/10.3390/electronics7100259.

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The effects of ultraviolet irradiation on luminescent centres in bismuth-doped (BDF) and bismuth/erbium co-doped (BEDF) optical fibers were examined in this study. The fibers were fabricated by modified chemical vapor deposition combining with atomic layer deposition method. The fibers were exposed to irradiation from a 193 nm pulsed wave argon fluoride laser, and an 830 nm wavelength laser diode pump source was employed for excitation. The experimental results showed that, for the BDF, the transmission loss was slightly reduced and the luminescence intensity was increased at the bismuth-relat

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Zvinowanda, Douglas, Chengedzai Mafini, and John D. Beneke. "Racial diversity in South African corporate boards and shareholder value creation: A decadal study." International Journal of Management and Sustainability 14, no. 2 (2025): 392–416. https://doi.org/10.18488/11.v14i2.4193.

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This study investigates the influence of board racial diversity (BRD) on shareholder value creation (SVC) of 95 non-financial companies listed on the Johannesburg Stock Exchange (JSE) from 2013 to 2022. The study employed a quantitative quasi-experimental method. The fixed effects model (FEM) was used to test the hypotheses. The results of linear FEM revealed that standard market value added was negatively influenced by the proportion of black directors (PBD), the Blau index for board racial diversity(BI_BRD) and dummies for skewed board (SB), tilted (TB) and balanced board (BB), while positiv

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