Special Issue "Proceedings of the International Conference in Mathematics and Applications 2020_Mahidol University"

A special issue of Computation (ISSN 2079-3197).

Deadline for manuscript submissions: closed (30 April 2021).

Special Issue Editors

Prof. Dr. Yongwimon Lenbury
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Guest Editor
Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand
Interests: nonlinear systems; differential equations; modelling of natural phenomena
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ravi P. Agarwal
grade E-Mail Website
Guest Editor
Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA
Interests: nonlinear analysis; differential and difference equations; fixed point theory; general inequalities
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Philip Broadbridge
E-Mail Website
Guest Editor
Dr. Dongwoo Sheen
E-Mail Website
Guest Editor
Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea
Interests: numerical analysis; scientific computation; application in fluid and solid mechanics; electrodynamics; math finance; math biology; fundamental nonconforming finite element methods; parallel algorithms based on Laplace transform methods

Special Issue Information

Dear Colleagues,

This issue is devoted to publishing significant advances in mathematical and computer modeling and simulation, including related research findings that are presented at the International Conference in Mathematics and Applications—Mahidol University to be organized by the Centre of Excellence in Mathematics, Commission on Higher Education, Thailand, on 18–20 December 2020. The goal of the conference is to bring together international researchers in order to promote, encourage and stimulate further research and highlight recent advances in the fields of applied mathematics that utilize mathematics and computational techniques as the springboard to develop a wide range of methodologies and tools applied in all fields of research.

This Special Issue invites original research papers that report on theoretical development and applications of the followings topics but are not limited to: ordinary differential equations, partial differential equations, functional differential equations, fractional differential equations, difference equations, delay differential equations, fractional difference equations, stochastic models, numerical techniques, generalized differential equations and impulsive differential equations.

Significant and relevant applications of the above are also encouraged. Specifically, research results in computational biology and medicine may include but not be limited to: mathematical modeling, simulation and prediction, mathematical modeling of pathways and genetic interactions, bioinformatics, and neuroscience computation, including neural modeling. Research results in computational chemistry may include but not be limited to: new theories and methodology, including their applications in molecular dynamics, computation of electronic structures, density functional theory, and design and characterization of materials with the computation method. Research results in computation in engineering may include but not be limited to: new theories, methodology and the application of computational fluid dynamics (CFD), optimization techniques and/or application of optimization to multidisciplinary systems, system identification and reduced order modeling, parallel algorithms and high performance computing.

This Special Issue’s main aim is to shine the lights on selected important research discoveries disseminated at the conference that are deemed to be of high quality and innovative value. So that these advances in research reported at the conference find more visibility and impact, it is important to have a venue for their publication. Computation is the best option through which full papers from the work presented at the conference have the opportunity to be peer reviewed and disseminated to a wider audience.

Dr. Yongwimon Lenbury
Dr. Ravi Agarwal
Dr. Philip Broadbridge
Dr. Dongwoo Sheen
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Computation is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Differential equations
  • Mathematical and numerical modeling
  • Computational techniques and applications
  • Statistical and stochastic models
  • Operations research and optimization

Published Papers (13 papers)

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Research

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Article
Integrating Data Mining Techniques for Naïve Bayes Classification: Applications to Medical Datasets
Computation 2021, 9(9), 99; https://0-doi-org.brum.beds.ac.uk/10.3390/computation9090099 - 13 Sep 2021
Viewed by 389
Abstract
In this study, we designed a framework in which three techniques—classification tree, association rules analysis (ASA), and the naïve Bayes classifier—were combined to improve the performance of the latter. A classification tree was used to discretize quantitative predictors into categories and ASA was [...] Read more.
In this study, we designed a framework in which three techniques—classification tree, association rules analysis (ASA), and the naïve Bayes classifier—were combined to improve the performance of the latter. A classification tree was used to discretize quantitative predictors into categories and ASA was used to generate interactions in a fully realized way, as discretized variables and interactions are key to improving the classification accuracy of the naïve Bayes classifier. We applied our methodology to three medical datasets to demonstrate the efficacy of the proposed method. The results showed that our methodology outperformed the existing techniques for all the illustrated datasets. Although our focus here was on medical datasets, our proposed methodology is equally applicable to datasets in many other areas. Full article
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Article
LMI-Based Results on Robust Exponential Passivity of Uncertain Neutral-Type Neural Networks with Mixed Interval Time-Varying Delays via the Reciprocally Convex Combination Technique
Computation 2021, 9(6), 70; https://0-doi-org.brum.beds.ac.uk/10.3390/computation9060070 - 10 Jun 2021
Cited by 1 | Viewed by 719
Abstract
The issue of the robust exponential passivity analysis for uncertain neutral-type neural networks with mixed interval time-varying delays is discussed in this work. For our purpose, the lower bounds of the delays are allowed to be either positive or zero adopting the combination [...] Read more.
The issue of the robust exponential passivity analysis for uncertain neutral-type neural networks with mixed interval time-varying delays is discussed in this work. For our purpose, the lower bounds of the delays are allowed to be either positive or zero adopting the combination of the model transformation, various inequalities, the reciprocally convex combination, and suitable Lyapunov–Krasovskii functional. A new robust exponential passivity criterion is received and formulated in the form of linear matrix inequalities (LMIs). Moreover, a new exponential passivity criterion is also examined for systems without uncertainty. Four numerical examples indicate our potential results exceed the previous results. Full article
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Article
Hybrid Feedback Control for Exponential Stability and Robust H Control of a Class of Uncertain Neural Network with Mixed Interval and Distributed Time-Varying Delays
Computation 2021, 9(6), 62; https://0-doi-org.brum.beds.ac.uk/10.3390/computation9060062 - 28 May 2021
Viewed by 822
Abstract
This paper is concerned the problem of robust H control for uncertain neural networks with mixed time-varying delays comprising different interval and distributed time-varying delays via hybrid feedback control. The interval and distributed time-varying delays are not necessary to be differentiable. The [...] Read more.
This paper is concerned the problem of robust H control for uncertain neural networks with mixed time-varying delays comprising different interval and distributed time-varying delays via hybrid feedback control. The interval and distributed time-varying delays are not necessary to be differentiable. The main purpose of this research is to estimate robust exponential stability of uncertain neural network with H performance attenuation level γ. The key features of the approach include the introduction of a new Lyapunov–Krasovskii functional (LKF) with triple integral terms, the employment of a tighter bounding technique, some slack matrices and newly introduced convex combination condition in the calculation, improved delay-dependent sufficient conditions for the robust H control with exponential stability of the system are obtained in terms of linear matrix inequalities (LMIs). The results of this paper complement the previously known ones. Finally, a numerical example is presented to show the effectiveness of the proposed methods. Full article
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Article
Application of the Exp-Function and Generalized Kudryashov Methods for Obtaining New Exact Solutions of Certain Nonlinear Conformable Time Partial Integro-Differential Equations
Computation 2021, 9(5), 52; https://0-doi-org.brum.beds.ac.uk/10.3390/computation9050052 - 26 Apr 2021
Viewed by 704
Abstract
The key objective of this paper is to construct exact traveling wave solutions of the conformable time second integro-differential Kadomtsev–Petviashvili (KP) hierarchy equation using the Exp-function method and the (2 + 1)-dimensional conformable time partial integro-differential Jaulent–Miodek (JM) evolution equation utilizing the generalized [...] Read more.
The key objective of this paper is to construct exact traveling wave solutions of the conformable time second integro-differential Kadomtsev–Petviashvili (KP) hierarchy equation using the Exp-function method and the (2 + 1)-dimensional conformable time partial integro-differential Jaulent–Miodek (JM) evolution equation utilizing the generalized Kudryashov method. These two problems involve the conformable partial derivative with respect to time. Initially, the conformable time partial integro-differential equations can be converted into nonlinear ordinary differential equations via a fractional complex transformation. The resulting equations are then analytically solved via the corresponding methods. As a result, the explicit exact solutions for these two equations can be expressed in terms of exponential functions. Setting some specific parameter values and varying values of the fractional order in the equations, their 3D, 2D, and contour solutions are graphically shown and physically characterized as, for instance, a bell-shaped solitary wave solution, a kink-type solution, and a singular multiple-soliton solution. To the best of the authors’ knowledge, the results of the equations obtained using the proposed methods are novel and reported here for the first time. The methods are simple, very powerful, and reliable for solving other nonlinear conformable time partial integro-differential equations arising in many applications. Full article
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Article
A Shoreline Evolution Model with a Groin Structure under Non-Uniform Breaking Wave Crest Impact
Computation 2021, 9(4), 42; https://0-doi-org.brum.beds.ac.uk/10.3390/computation9040042 - 26 Mar 2021
Viewed by 759
Abstract
Beach erosion is a natural phenomenon that is not compensated by depositing fresh material on the shoreline while transporting sand away from the shoreline. There are three phenomena that have a serious influence on the coastal structure, such as increases in flooding, accretion, [...] Read more.
Beach erosion is a natural phenomenon that is not compensated by depositing fresh material on the shoreline while transporting sand away from the shoreline. There are three phenomena that have a serious influence on the coastal structure, such as increases in flooding, accretion, and water levels. In addition, the prediction of coastal evolution is used to investigate the topography of the beach. In this research, we present a one-dimensional mathematical model of shoreline evolution, and the parameters that influence this model are described on a monthly basis over a period of one year. Consideration is given to the wave crest impact model for evaluating the impact of the wave crest at that stage. It focuses on the evolution of the shoreline in environments where groins are installed on both sides. The initial and boundary condition setting techniques are proposed by the groins and their environmental parameters. The non-uniform influence of the crest of the breaking wave is so often considered. We then used the traditional forward time centered space technique and the Saulyev finite difference technique to estimate the monthly evolution of the shoreline for each year. Full article
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Article
Effect of Additional Order in Two-Stage Supply Chain Contract under the Demand Uncertainty
Computation 2021, 9(3), 37; https://0-doi-org.brum.beds.ac.uk/10.3390/computation9030037 - 22 Mar 2021
Viewed by 631
Abstract
In this work, mathematical models are formulated in order to investigate the effect of the additional order on the expected total profit of a two-stage supply chain. A multi-period buyback contract between a supplier and a retailer under the demand uncertainty is considered. [...] Read more.
In this work, mathematical models are formulated in order to investigate the effect of the additional order on the expected total profit of a two-stage supply chain. A multi-period buyback contract between a supplier and a retailer under the demand uncertainty is considered. Under the contract, an advance order is submitted to the supplier in advance when the demand is unknown, and an additional order can be made at the beginning of each period after the previous period demand is realized. The impact of the coordination on the supply chain’s expected total profit is also considered. The results show that the additional order does not always increases the supply chain profit. The additional order increases the supply chain profit only when both the retailer and supplier are coordinated. Under the decentralized system with the buyback contract, the retailer tends to order less in an advance order to reduce the risk. This leads to the higher cost due the additional order after the demand is realized. As a result, it is lowers the supply chain profit. Moreover, the sensitivity analysis is performed using numerical studies in order to observe the behavior of the expected total profit of the supply chain. Full article
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Article
An Application of Optimal Control to Sugarcane Harvesting in Thailand
Computation 2021, 9(3), 36; https://0-doi-org.brum.beds.ac.uk/10.3390/computation9030036 - 19 Mar 2021
Viewed by 715
Abstract
The sugar industry is of great importance to the Thai economy. In general, the government sets sugarcane prices at the beginning of each harvesting season based on type (fresh or fired), sweetness (sugar content) and gross weight. The main aim of the present [...] Read more.
The sugar industry is of great importance to the Thai economy. In general, the government sets sugarcane prices at the beginning of each harvesting season based on type (fresh or fired), sweetness (sugar content) and gross weight. The main aim of the present research is to use optimal control to find optimal sugarcane harvesting policies for fresh and fired sugarcane for the four sugarcane producing regions of Thailand, namely North, Central, East and North-east, for harvesting seasons 2012/13, 2013/14, 2014/15, 2017/18 and 2018/19. The optimality problem is to determine the harvesting policy which gives maximum profit to the farmers subject to constraints on the maximum amount that can be cut in each day, where a harvesting policy is defined as the amount of each type of sugarcane harvested and delivered to the sugar factories during each day of a harvesting season. The results from the optimal control methods are also compared with results from three optimization methods, namely bi-objective, linear programming and quasi-Newton. The results suggest that discrete optimal control is the most effective of the five methods considered. The data used in this paper were obtained from the Ministry of Industry and the Ministry of Agriculture and Co-operatives of the Royal Thai government. Full article
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Article
Application of the Generalized Laplace Homotopy Perturbation Method to the Time-Fractional Black–Scholes Equations Based on the Katugampola Fractional Derivative in Caputo Type
Computation 2021, 9(3), 33; https://0-doi-org.brum.beds.ac.uk/10.3390/computation9030033 - 12 Mar 2021
Viewed by 850
Abstract
In the finance market, the Black–Scholes equation is used to model the price change of the underlying fractal transmission system. Moreover, the fractional differential equations recently are accepted by researchers that fractional differential equations are a powerful tool in studying fractal geometry and [...] Read more.
In the finance market, the Black–Scholes equation is used to model the price change of the underlying fractal transmission system. Moreover, the fractional differential equations recently are accepted by researchers that fractional differential equations are a powerful tool in studying fractal geometry and fractal dynamics. Fractional differential equations are used in modeling the various important situations or phenomena in the real world such as fluid flow, acoustics, electromagnetic, electrochemistry and material science. There is an important question in finance: “Can the fractional differential equation be applied in the financial market?”. The answer is “Yes”. Due to the self-similar property of the fractional derivative, it can reply to the long-range dependence better than the integer-order derivative. Thus, these advantages are beneficial to manage the fractal structure in the financial market. In this article, the classical Black–Scholes equation with two assets for the European call option is modified by replacing the order of ordinary derivative with the fractional derivative order in the Caputo type Katugampola fractional derivative sense. The analytic solution of time-fractional Black–Scholes European call option pricing equation with two assets is derived by using the generalized Laplace homotopy perturbation method. The used method is the combination of the homotopy perturbation method and generalized Laplace transform. The analytic solution of the time-fractional Black–Scholes equation is carried out in the form of a Mittag–Leffler function. Finally, the effects of the fractional-order in the Caputo type Katugampola fractional derivative to change of a European call option price are shown. Full article
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Article
Variable Coefficient Exact Solutions for Some Nonlinear Conformable Partial Differential Equations Using an Auxiliary Equation Method
Computation 2021, 9(3), 31; https://0-doi-org.brum.beds.ac.uk/10.3390/computation9030031 - 10 Mar 2021
Viewed by 736
Abstract
The objective of this present paper is to utilize an auxiliary equation method for constructing exact solutions associated with variable coefficient function forms for certain nonlinear partial differential equations (NPDEs) in the sense of the conformable derivative. Utilizing the specific fractional transformations, the [...] Read more.
The objective of this present paper is to utilize an auxiliary equation method for constructing exact solutions associated with variable coefficient function forms for certain nonlinear partial differential equations (NPDEs) in the sense of the conformable derivative. Utilizing the specific fractional transformations, the conformable derivatives appearing in the original equation can be converted into integer order derivatives with respect to new variables. As for applications of the method, we particularly obtain variable coefficient exact solutions for the conformable time (2 + 1)-dimensional Kadomtsev–Petviashvili equation and the conformable space-time (2 + 1)-dimensional Boussinesq equation. As a result, the obtained exact solutions for the equations are solitary wave solutions including a soliton solitary wave solution and a bell-shaped solitary wave solution. The advantage of the used method beyond other existing methods is that it provides variable coefficient exact solutions covering constant coefficient ones. In consequence, the auxiliary equation method based on setting all coefficients of an exact solution as variable function forms can be more extensively used, straightforward and trustworthy for solving the conformable NPDEs. Full article
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Article
Traveling Wave Solutions of a Four Dimensional Reaction-Diffusion Model for Porcine Reproductive and Respiratory Syndrome with Time Dependent Infection Rate
Computation 2021, 9(3), 30; https://0-doi-org.brum.beds.ac.uk/10.3390/computation9030030 - 09 Mar 2021
Viewed by 671
Abstract
Porcine reproductive and respiratory syndrome virus (PRRSV) causes reproductive failure in sows and respiratory disease in piglets and growing pigs. The disease rapidly spreads in swine populations, making it a serious problem causing great financial losses to the swine industry. However, past mathematical [...] Read more.
Porcine reproductive and respiratory syndrome virus (PRRSV) causes reproductive failure in sows and respiratory disease in piglets and growing pigs. The disease rapidly spreads in swine populations, making it a serious problem causing great financial losses to the swine industry. However, past mathematical models used to describe the spread of the disease have not yielded sufficient understanding of its spatial transmission. This work has been designed to investigate a mathematical model for the spread of PRRSV considering both time and spatial dimensions as well as the observed decline in infectiousness as time progresses. Moreover, our model incorporates into the dynamics the assumption that some members of the infected population may recover from the disease and become immune. Analytical solutions are derived by using the modified extended hyperbolic tangent method with the introduction of traveling wave coordinate. We also carry out a stability and phase analysis in order to obtain a clearer understanding of how PRRSV spreads spatially through time. Full article
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Article
Transient Pressure-Driven Electroosmotic Flow through Elliptic Cross-Sectional Microchannels with Various Eccentricities
Computation 2021, 9(3), 27; https://0-doi-org.brum.beds.ac.uk/10.3390/computation9030027 - 01 Mar 2021
Viewed by 681
Abstract
The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution [...] Read more.
The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions. Full article
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Article
Improved Stability Criteria on Linear Systems with Distributed Interval Time-Varying Delays and Nonlinear Perturbations
Computation 2021, 9(2), 22; https://0-doi-org.brum.beds.ac.uk/10.3390/computation9020022 - 21 Feb 2021
Viewed by 714
Abstract
The problem of delay-range-dependent stability analysis for linear systems with distributed time-varying delays and nonlinear perturbations is studied without using the model transformation and delay-decomposition approach. The less conservative stability criteria are obtained for the systems by constructing a new augmented Lyapunov–Krasovskii functional [...] Read more.
The problem of delay-range-dependent stability analysis for linear systems with distributed time-varying delays and nonlinear perturbations is studied without using the model transformation and delay-decomposition approach. The less conservative stability criteria are obtained for the systems by constructing a new augmented Lyapunov–Krasovskii functional and various inequalities, which are presented in terms of linear matrix inequalities (LMIs). Four numerical examples are demonstrated for the results given to illustrate the effectiveness and improvement over other methods. Full article

Review

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Review
Origin of Irrational Numbers and Their Approximations
Computation 2021, 9(3), 29; https://0-doi-org.brum.beds.ac.uk/10.3390/computation9030029 - 09 Mar 2021
Viewed by 756
Abstract
In this article a sincere effort has been made to address the origin of the incommensurability/irrationality of numbers. It is folklore that the starting point was several unsuccessful geometric attempts to compute the exact values of 2 and π. Ancient records substantiate [...] Read more.
In this article a sincere effort has been made to address the origin of the incommensurability/irrationality of numbers. It is folklore that the starting point was several unsuccessful geometric attempts to compute the exact values of 2 and π. Ancient records substantiate that more than 5000 years back Vedic Ascetics were successful in approximating these numbers in terms of rational numbers and used these approximations for ritual sacrifices, they also indicated clearly that these numbers are incommensurable. Since then research continues for the known as well as unknown/expected irrational numbers, and their computation to trillions of decimal places. For the advancement of this broad mathematical field we shall chronologically show that each continent of the world has contributed. We genuinely hope students and teachers of mathematics will also be benefited with this article. Full article
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