The successive differentiation computer-assisted method for solving well-known scientific and engineering models

2018 ◽  
Vol 28 (12) ◽  
pp. 2862-2873
Author(s):  
Suheil Khuri ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Problem Solving ◽  
Differential Equations ◽  
Undergraduate Students ◽  
Variable Coefficients ◽  
Abel Equation ◽  
Computer Assisted ◽  
Computational Tool ◽  
Content Type ◽  
Wide Range ◽  
Linear And Nonlinear

PurposeOrdinary differential equations (ODEs) are widely used in the engineering curriculum. They model a spectrum of interesting physical problems that arise in engineering disciplines. Studies of different types of ODEs are determined by engineering applications. Various techniques are used to solve practical differential equations problems. This paper aims to present a computational tool or a computer-assisted technique aimed at tackling ODEs. This method is usually not taught and/or not accessible to undergraduate students. The aim of this strategy is to help the readers to develop an effective and relatively novel problem-solving skill. Because of the drudgery of hand computations involved, the method requires the need to use computers packages. In this work, the successive differentiation method (SDM) for solving linear and nonlinear and homogeneous or non-homogeneous ODEs is presented. The algorithm uses the successive differentiation of any given ODE to determine the values of the function’s derivatives at a single point, mostly x = 0. The obtained values are used to construct the Taylor series of the solution of the examined ODE. The algorithm does not require any new assumption, hence handles the problem in a direct manner. The power of the method is emphasized by testing a variety of models with distinct orders, with constant and variable coefficients. Most of the symbolic and numerical computations can be carried out using computer algebra systems.Design/methodology/approachThis study presents a computational tool or a computer-assisted technique aimed at tackling ODEs. This method is usually not taught and/or not accessible to undergraduate students. The aim of this strategy is to help the readers to develop an effective and relatively novel problem-solving skill. Because of the drudgery of hand computations involved, the method requires the need to use computers packages.FindingsThis method is applied to a variety of well-known equations, such as the Bernoulli equation, the Riccati equation, the Abel equation and the second-order Euler equation, some with constant and variable coefficients. SDM handles linear and nonlinear and homogeneous or nonhomogeneous ODEs in a direct manner without any need to restrictive conditions. The method works effectively to the Volterra integral equations, as will be discussed in a coming work.Originality/valueThe method can be extended to a wide range of engineering problems that are modeled by differential equations. The method is simple and novel and highly accurate.

scholarly journals Evaluating undergraduate research conferences as vehicles for novice researcher development

2016 ◽  
Vol 7 (2) ◽  
pp. 159-177 ◽  
Author(s):  
Pauline Kneale ◽  
Andrew Edwards-Jones ◽  
Helen Walkington ◽  
Jennifer Hill
Keyword(s):  
Undergraduate Students ◽  
Undergraduate Research ◽  
Skills Development ◽  
Learning Context ◽  
Content Type ◽  
Research Conference ◽  
Researcher Development ◽  
Development Framework ◽  
Wide Range ◽  
The Impact

Purpose This paper aims to focus on the undergraduate research conference as its sphere of study and investigate the impact of significance of participation and socialisation in such activities on student attitudes and professional development. Using situated learning to theoretically position the undergraduate research conference as an authentic learning context, connection is also made with the concept of graduate attributes. Design/methodology/approach The Vitae (2014) Researcher Development Framework (RDF) is used to provide a template for charting the experiences and development of undergraduate students as researchers. This can be applied to short-term activities and programmes and to long-term career plans. The insights from 90 undergraduate students participating in three national undergraduate research conferences were obtained through interviews, and thematically analysed to map the students’ skills development against the RDF criteria. Findings Three main aspects of undergraduate research conference participation were considered particularly important by the students: the value of paper presentations, the value of poster presentations and the value of the overall conference experience. Within these themes, participants identified a wide range of skills and attributes they felt they had developed as a result of either preparing for or participating in the conferences. The majority of these skills and attributes could be mapped against the different domains of the RDF, using a public engagement lens for comparing actual with expected developmental areas. Research limitations/implications This research helps undergraduate research conference organisers construct programme content and form it in such a way that students’ skill development can be maximised prior to, and during, the course of an event. Learning developers can also use these findings to help understand the support needs of students preparing to deliver papers at such conferences. So far, little empirical research has examined students’ skills development within the undergraduate research conference arena. Originality/value The outcomes of this study show the diversity of the skills that students developed and the value of the conference format for offering networking practice and enhancing the communication skills which employers value.

Numerical solutions for unsteady boundary layer flow of a dusty fluid past a permeable stretching/shrinking surface with particulate viscous effect

2018 ◽  
Vol 28 (6) ◽  
pp. 1374-1391 ◽  
Author(s):  
Rohana Abdul Hamid ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Unsteady Flow ◽  
Fluid Particle ◽  
Dust Particles ◽  
Physical Parameters ◽  
Suction Parameter ◽  
Content Type ◽  
Dusty Fluid ◽  
Wide Range

Purpose This present aims to present the numerical study of the unsteady stretching/shrinking flow of a fluid-particle suspension in the presence of the constant suction and dust particle slip on the surface. Design/methodology/approach The governing partial differential equations for the two phases flows of the fluid and the dust particles are reduced to the pertinent ordinary differential equations using a similarity transformation. The numerical results are obtained using the bvp4c function in the Matlab software. Findings The results revealed that in the decelerating shrinking flow, the wall skin friction is higher in the dusty fluid when compared to the clean fluid. In addition, the effect of the fluid-particle interaction parameter to the fluid-phase can be seen more clearly in the shrinking flow. Other non-dimensional physical parameters such as the unsteadiness parameter, the mass suction parameter, the viscosity ratio parameter, the particle slip parameter and the particle loading parameter are also considered and presented in figures. Further, the second solution is discovered in this problem and the solution expanded with higher unsteadiness and suction values. Hence, the stability analysis is performed, and it is confirmed that the second solution is unstable. Practical implications In practice, the flow conditions are commonly varying with time; thus, the study of the unsteady flow is very crucial and useful. The problem of unsteady flow of a dusty fluid has a wide range of possible applications such as in the centrifugal separation of particles, sedimentation and underground disposable of radioactive waste materials. Originality/value Even though the problem of dusty fluid has been broadly investigated, limited discoveries can be found over an unsteady shrinking flow. Indeed, this paper managed to obtain the second (dual) solutions, and stability analysis is performed. Furthermore, the authors also considered the artificial particle-phase viscosity, which is an important term to study the particle-particle and particle-wall interactions. With the addition of this term, the effects of the particle slip and suction parameters can be investigated. Very few studies in the dusty fluid embedded this parameter in their problems.

Frequency response analysis of periodically time varying circuits

2018 ◽  
Vol 37 (3) ◽  
pp. 1204-1213
Author(s):  
Igor Korotyeyev
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Steady State Solution ◽  
Variable Coefficients ◽  
State Solution ◽  
Response Analysis ◽  
Time Varying ◽  
Content Type ◽  
Frequency Responses ◽  
Definition Of

Purpose The purpose of this paper is to introduce a method for the analysis of steady-state processes in periodically time varying circuits. The method is based on a new definition of frequency responses for periodic time-varying circuits. Design/methodology/approach Processes in inverter circuits are often described by differential equations with periodically variable coefficients and forcing functions. To obtain a steady-state periodic solution, the expansion of differential equations into a domain of two independent variables of time is made. To obtain differential equations with constant coefficients the Lyapunov transformation is applied. The two-dimensional Laplace transform is used to find a steady-state solution. The steady-state solution is obtained in the form of the double Fourier series. The transfer function and frequency responses for the inverter circuit are introduced. Findings A set of frequency characteristics are defined. An example of a boost inverter is considered, and a set of frequency responses for voltage and current are presented. These responses show a resonance that is missed if the averaged state-space method is used. Originality/value A new definition of frequency responses is presented. On the basis of frequency responses, a modulation strategy and filters can be chosen to improve currents and voltages.

Objectives and measures of performance of Islamic microfinance banks in Indonesia: the stakeholders' perspectives

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Taufik Akbar ◽  
A.K. Siti-Nabiha
Keyword(s):  
Islamic Law ◽  
Well Being ◽  
Empirical Literature ◽  
Future Research ◽  
Computer Assisted ◽  
Content Type ◽  
Wide Range ◽  
External Stakeholders ◽  
Islamic Microfinance ◽  
Measures Of Performance

PurposeThis study investigates both internal and external stakeholders' views on the objectives and measures of performance of Indonesian Islamic microfinance banks (IMFBs).Design/methodology/approachThis study uses a qualitative approach. In-depth interviews were conducted with a wide range of internal and external stakeholders of IMFBs in Indonesia. The primary stakeholders interviewed comprised the board of directors of IMFBs located in several provinces in Indonesia, including rural and urban areas. The external stakeholders were the regulators/supervisors, represented by the Indonesian Financial Services Authority and Sharīʿah advisors of the National Sharīʿah Board as well as Muslim scholars. The data were analysed using CAQDAS, a computer-assisted tool for qualitative analysis.FindingsThe objectives of the IMFBs are seen to represent more than profits or economic well-being. Their objectives also comprise spirituality and daʿwah (Islamic propagation). Daʿwah is conducted through the provision of funding and services that are aligned with Sharīʿah (Islamic law), the dissemination of information about Islamic financing, which is based on Islamic values and principles, and the payment of zakat (Islamic alms) and charitable contributions. The measures of performance are considered to be more holistic than those of conventional banks. Profit and growth are deemed important as the means to achieve social well-being objectives.Research limitations/implicationsBetter insights into the objectives and measures of IMFBs could be achieved from interviews with other stakeholder categories, such as customers and the community. This could be the focus of future research.Originality/valueThis study added a new discussion to the limited empirical literature on IMFBs by investigating the views of stakeholders on the objectives and performance of IMFBs in Indonesia.

A Problem-Solving Approach to the Introduction to Ordinary Differential Equations for Undergraduate Students at an American Two-year College

2019 ◽  
pp. 183-188
Author(s):  
John Gordon
Keyword(s):  
New York ◽  
Problem Solving ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Undergraduate Students ◽  
Homogeneous Equation ◽  
Introductory Course ◽  
Two Year College ◽  
Course Material ◽  
And Mathematics

Undergraduate students in STEM (Science, Technology, Engineering, and Mathematics) at City University of New York (CUNY)-Queensborough Community College (QCC) working toward a baccalaureate degree at one of CUNY’s senior colleges are required to take an introductory course in ordinary differential equations (ODE). Faculty in the Mathematics Department at QCC are experimenting with a problem-solving approach to this course in which students engage in learning course material through the development of mathematical models of real-world problems. The results seem promising and we outline them in this paper. Key-Words: First-order, linear system, integrating factor, homogeneous equation, research-based.

Solving the fractional heat-like and wave-like equations with variable coefficients utilizing the Laplace homotopy method

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Muhammad Nadeem ◽  
Shao-Wen Yao
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Homotopy Perturbation Method ◽  
Variable Coefficients ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Content Type ◽  
The Laplace Transform ◽  
First Time

Purpose This paper aims to suggest the approximate solution of time fractional heat-like and wave-like (TFH-L and W-L) equations with variable coefficients. The proposed scheme shows that the results are very close to the exact solution. Design/methodology/approach First with the help of some basic properties of fractional derivatives, a scheme that has the capability to solve fractional partial differential equations is constructed. Then, TFH-L and W-L equations with variable coefficients are solved by this scheme, which yields results very close to the exact solution. The derived results demonstrate that this scheme is very effective. Finally, the convergence of this method is discussed. Findings A traditional method is combined with the Laplace transform to construct this scheme. To decompose the nonlinear terms, this paper introduces the homotopy perturbation method with He’s polynomials and thus the solution is provided in the form of a series that converges to the exact solution very quickly. Originality/value The proposed approach is original and very effective because this approach is, to the authors’ knowledge, used for the first time very successfully to tackle the fractional partial differential equations, which are of great interest.

Natural Frequencies of the Bias Tire

1976 ◽  
Vol 4 (2) ◽  
pp. 86-114 ◽  
Author(s):  
M. Hirano ◽  
T. Akasaka
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Composite Structure ◽  
Natural Frequencies ◽  
Variable Coefficients ◽  
System Of Differential Equations ◽  
Inflation Pressure ◽  
Point Collocation ◽  
Membrane Shell ◽  
Wide Range

Abstract The lowest natural frequencies of a bias tire under inflation pressure are deduced by assuming the bias tire as a composite structure of a bias-laminated, toroidal membrane shell and rigorously taking three displacement components into consideration. The point collocation method is used to solve a derived system of differential equations with variable coefficients. It is found that the lowest natural frequencies calculated for two kinds of bias tire agree well with the corresponding experimental results in a wide range of inflation pressure.

E-complaint tracking and online problem-solving strategies in hospitality management

2017 ◽  
Vol 8 (3) ◽  
pp. 372-394 ◽  
Author(s):  
Ilker Sahin ◽  
Mustafa Gulmez ◽  
Olgun Kitapci
Keyword(s):  
Problem Solving ◽  
Public Relations ◽  
Online Reviews ◽  
Corporate Identity ◽  
Hospitality Management ◽  
Research Approach ◽  
Context Analysis ◽  
Content Type ◽  
Wide Range ◽  
Problem Solving Strategies

Purpose This research aims to scrutinize the negative reviews regarding the 5-star chain hotels and the e-responses on TripAdvisor, to categorize the complaints declared in the review texts, to provide better understanding of the online problem-solving methods of hotels and their corporate approach to e-complaints and to reveal the post-vacation electronic word-of-mouth (e-WOM) behaviours of the complaining tourists. Design/methodology/approach Within the scope of this research, 404 negative reviews and 364 e-responses are subject to an extensive content analysis. A total of 1,655 tourist e-complaints which were mentioned in the negative online reviews are categorized according to their subject matters and grouped under main themes. The e-responses of hotels and statements of e-complaining tourists regarding post-vacation experience are analysed in detail based on a qualitative research approach. Findings As a result of the research, 82 sub-themes within 11 complaint categories are determined, and it is found out that the e-complaints mainly focus on “food and beverage services”, “room comfort” and “hotel staff”. The hotel management mainly implemented problem-solving strategies such as “request for future patronage, a recovery plan as a result of the detailed analysis of the problem and warning to the relevant department performing poor service” as well as giving unsatisfactory “cliché responses”. Dissatisfied tourists performed negative e-WOM behaviours by using abusing expressions in review text, recommending different hotel alternatives, failing to recommend the hotel and expressing that they would not return. Originality/value Combing through negative e-reviews which include wide range of complaints of disappointed tourists and the statements which reveal post-vacation tendencies and feelings, the e-responses of hotels that are providing insight regarding the corporate approach to negative feedbacks and formation of post-vacation relations between the hotel and customers, the paper adopts a qualitative and utilitarian approach. The originality of the paper stems from its elaborative context analysis and balanced comparison of three 5-star luxury chain resort hotels located on the shores of the Mediterranean with almost similar quality standards and guest relations/public relations (GR/PR) departments that represent corporate identity. To this respect, the research is thought to be original in quality and can fill out the gap in the tourism literature. Presenting conceptual framework and practical information, the paper is predicted to guide the future studies, tourism marketers, travel consultants, PR/GR staff and managers employed in hospitality businesses.

Undergraduate African–American student’s experience of racial microaggressions on a primarily white campus

2018 ◽  
Vol 12 (3) ◽  
pp. 267-277
Author(s):  
Kyle J. Brezinski ◽  
John Laux ◽  
Christopher Roseman ◽  
Caroline O’Hara ◽  
Shanda Gore
Keyword(s):  
African American ◽  
Undergraduate Students ◽  
Racial Microaggressions ◽  
College Retention ◽  
Retention Rates ◽  
Dropping Out ◽  
Content Type ◽  
Staff Members ◽  
Wide Range ◽  
The Relationship

Purpose The purpose of this study is to investigate the relationship between African–American undergraduate students, racial microaggressions (RMAs) and college retention rates. Design/methodology/approach Data were obtained from a survey given out to African–American undergraduate students, recruited from a large, midwestern, predominantly white public university (n = 53). Findings The results indicate that students did experience a wide range of microaggressions. Furthermore, the data revealed a statistically significant relationship between the participants’ perceptions that others viewed them as if they were foreigners and did not belong to the place and the participants’ thoughts about dropping out during the ongoing semester [r(51) = 0.338, p = 0.05]. The results suggest that African–Americans frequently experience RMAs while on campus but these experiences are not significantly tied to their intentions to complete the ongoing semester or return for the subsequent semester. Practical implications This study shows that African–American students felt disconnected from the campus that they attend. This information may allow for faculty and staff members to assist in making students feel more welcomed and included in the classroom and on campus. Originality/value This is one of the few studies to provide evidence of the relationships between African–American undergraduate students, RMAs and college retention rates. In addition, most studies looking at the relationship between RMAs and retention are qualitative in nature. The use of a quantitative approach helps us eliminating possible observer bias and increasing sample size.

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