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Applications and Applied Mathematics: An International Journal (AAM)

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Articles 301 - 330 of 702

Full-Text Articles in Applied Mathematics

Mhd Boundary Layer Slip Flow Over A Flat Plate With Soret And Dufour Effects, B. Shashidar Reddy, K. Saritha Mar 2019

Mhd Boundary Layer Slip Flow Over A Flat Plate With Soret And Dufour Effects, B. Shashidar Reddy, K. Saritha

Applications and Applied Mathematics: An International Journal (AAM)

The present paper studies the effects of Soret and Dufour on MHD boundary layer slip flow over a flat plate. The governing partial differential equations are converted to a set of nonlinear ordinary differential equations by using similarity transformations. Then, these equations are solved numerically by implicit Finite Difference Scheme. The numerical solutions for Velocity, Temperature and Concentration profiles for the related essential physical parameters are visualized through graphs and discussed. Results show that the velocity rises whereas the temperature and concentration reduces with the respective slip parameters. The increase in Soret number or decrease in Dufour number reduces the …

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Brownian Motion And Thermophoresis Effects On Casson Nanofluid Over A Chemically Reacting Stretching Sheet With Inclined Magnetic Field, D. Gopal, N. Kishan Mar 2019

Brownian Motion And Thermophoresis Effects On Casson Nanofluid Over A Chemically Reacting Stretching Sheet With Inclined Magnetic Field, D. Gopal, N. Kishan

Applications and Applied Mathematics: An International Journal (AAM)

The contemporary study explores the impact of thermophoresis and Brownian motion on two-dimensional magnetohydrodynamic boundary layer flow of Casson nanofluid over a chemically reacting stretching sheet. To control the heat and mass transport phenomena we also included the thermophoresis diffusion coefficient, Brownian motion parameter, and thermal radiation. The regular physical governing systems of partial differential equations are transmogrifying into ordinary differential equations. The transmogrifying governing equations are checked numerically by using Runge-Kutta-Fehlberg method. The numerical solutions for heterogeneous governing parameters such as Schmidt number, Joule heating parameter, and permeability parameter, chemical reaction parameters on velocity, temperature, and concentration profiles were …

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Joule Heat Parameter Effects On Unsteady Mhd Flow Over A Stretching Sheet With Viscous Dissipation And Heat Source, Srinivas Maripala, Kishan Naikoti Mar 2019

Joule Heat Parameter Effects On Unsteady Mhd Flow Over A Stretching Sheet With Viscous Dissipation And Heat Source, Srinivas Maripala, Kishan Naikoti

Applications and Applied Mathematics: An International Journal (AAM)

In the present investigation, we studied the effects of heat source and Joule heating parameter on unsteady magneto-hydro-dynamic and heat transfer of a fluid flow over a radiating stretching sheet. The governing partial differential equations of nonlinear with boundary conditions are solved numerically by implicit finite difference method with Gauss Seidel iteration scheme. The obtained numerical solutions of velocity and temperature profiles are discussed and represented graphically. The effects of various parameters on the velocity and temperature profiles are shown graphically and numerical values of physical quantities such as the skin friction coefficient and the local Nusselt number are presented …

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Optimal Homotopy Asymptotic Solution For Thermal Radiation And Chemical Reaction Effects On Electrical Mhd Jeffrey Fluid Flow Over A Stretching Sheet Through Porous Media With Heat Source, Gossaye Aliy, Naikoti Kishan Mar 2019

Optimal Homotopy Asymptotic Solution For Thermal Radiation And Chemical Reaction Effects On Electrical Mhd Jeffrey Fluid Flow Over A Stretching Sheet Through Porous Media With Heat Source, Gossaye Aliy, Naikoti Kishan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the problem of thermal radiation and chemical reaction effects on electrical MHD Jeffrey fluid flow over a stretching surface through a porous medium with the heat source is presented. We obtained the approximate analytical solution of the nonlinear differential equations governing the problem using the Optimal Homotopy Asymptotic Method (OHAM). Comparison of results has been made with the numerical solutions from the literature, and a very good agreement has been observed. Subsequently, effects of governing parameters of the velocity, temperature and concentration profiles are presented graphically and discussed.

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Mhd Boundary Layer Flow Of Darcy-Forchheimer Mixed Convection In A Nanofluid Saturated Porous Media With Viscous Dissipation, S. Jagadha, P. Amrutha Mar 2019

Mhd Boundary Layer Flow Of Darcy-Forchheimer Mixed Convection In A Nanofluid Saturated Porous Media With Viscous Dissipation, S. Jagadha, P. Amrutha

Applications and Applied Mathematics: An International Journal (AAM)

The steady laminar viscous incompressible nanofluid flow of mixed convection and mass transfer about an isothermal vertical flat plate embedded in Darcy porous medium in the presence of magnetic field and viscous dissipation is analyzed. The governing partial differential equations are converted into ordinary differential equations by similarity transformations. The coupled nonlinear ordinary differential equations are linearized by Quasi-linearization technique. The linear ordinary differential equations are solved by using implicit finite difference scheme with the help of C-programming. Numerical calculations are carried out for different values of dimensionless parameter such as magnetic field, mixed convection parameter, inertia parameter, buoyancy ratio …

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Active Control Of A Forced Mindlin-Type Beam, Kenan Yildirim Feb 2019

Active Control Of A Forced Mindlin-Type Beam, Kenan Yildirim

Applications and Applied Mathematics: An International Journal (AAM)

In this study, optimal dynamic response control of a forced Mindlin-type beam is studied. The beam under consideration, which consists of central host layer and two piezoelectric patch actuators bonded on perfectly to both sides of the beam. It is assumed that the beam is subject to the forcing function, initially at rest and undeformed. Hence, a forced Mindlin-type beam is considered for active vibration control. For this aim, well-posedness and controllability of the system are presented. Performance index functional to be minimized by using minimum level of control voltage consists of a weighted quadratic functions of displacement and velocity …

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Transient Solution Of An M/M/1 Retrial Queue With Reneging From Orbit, A. Azhagappan, E. Veeramani, W. Monica, K. Sonabharathi Dec 2018

Transient Solution Of An M/M/1 Retrial Queue With Reneging From Orbit, A. Azhagappan, E. Veeramani, W. Monica, K. Sonabharathi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the transient behavior of an M/M/1 retrial queueing model is analyzed where the customers in the orbit possess the reneging behavior. There is no waiting room in the system for the arrivals. If the server is not free when the occurrence of an arrival, the arriving customer moves to the waiting group, known as orbit and retries for his service. If the server is idle when an arrival occurs (either coming from outside the queueing system or from the waiting group), the arrival immediately gets the service and leaves the system. Each individual customer in the orbit, …

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An M^X/G(A,B)/1 Queue With Breakdown And Delay Time To Two Phase Repair Under Multiple Vacation, G. Ayyappan, M. Nirmala Dec 2018

An M^X/G(A,B)/1 Queue With Breakdown And Delay Time To Two Phase Repair Under Multiple Vacation, G. Ayyappan, M. Nirmala

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider an Mx /G(a,b)/1 queue with active breakdown and delay time to two phase repair under multiple vacation policy. A batch of customers arrive according to a compound Poisson process. The server serves the customers according to the “General Bulk Service Rule” (GBSR) and the service time follows a general (arbitrary) distribution. The server is unreliable and it may breakdown at any instance. As the result of breakdown, the service is suspended, the server waits for the repair to start and this waiting time is called as „delay time‟ and is assumed to follow general …

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Fibonacci And Lucas Differential Equations, Esra Erkus-Duman, Hakan Ciftci Dec 2018

Fibonacci And Lucas Differential Equations, Esra Erkus-Duman, Hakan Ciftci

Applications and Applied Mathematics: An International Journal (AAM)

The second-order linear hypergeometric differential equation and the hypergeometric function play a central role in many areas of mathematics and physics. The purpose of this paper is to obtain differential equations and the hypergeometric forms of the Fibonacci and the Lucas polynomials. We also write again these polynomials by means of Olver’s hypergeometric functions. In addition, we present some relations between these polynomials and the other well-known functions.

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Approximate Analytical Solutions Of Space-Fractional Telegraph Equations By Sumudu Adomian Decomposition Method, Hasib Khan, Cemil Tunç, Rahmat A. Khan, Akhtyar G. Shirzoi, Aziz Khan Dec 2018

Approximate Analytical Solutions Of Space-Fractional Telegraph Equations By Sumudu Adomian Decomposition Method, Hasib Khan, Cemil Tunç, Rahmat A. Khan, Akhtyar G. Shirzoi, Aziz Khan

Applications and Applied Mathematics: An International Journal (AAM)

The main goal in this work is to establish a new and efficient analytical scheme for space fractional telegraph equation (FTE) by means of fractional Sumudu decomposition method (SDM). The fractional SDM gives us an approximate convergent series solution. The stability of the analytical scheme is also studied. The approximate solutions obtained by SDM show that the approach is easy to implement and computationally very much attractive. Further, some numerical examples are presented to illustrate the accuracy and stability for linear and nonlinear cases.

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Thermoelastic Stress Analysis Of A Functionally Graded Transversely Isotropic Hollow Cylinder In Elliptical Coordinates, Tara Dhakate, Vinod Varghese, Lalsingh Khalsa Dec 2018

Thermoelastic Stress Analysis Of A Functionally Graded Transversely Isotropic Hollow Cylinder In Elliptical Coordinates, Tara Dhakate, Vinod Varghese, Lalsingh Khalsa

Applications and Applied Mathematics: An International Journal (AAM)

This paper is concerned with the axisymmetric thermoelastic problem to investigate the influence of nonlinear heat conduction equation, displacement functions and thermal stresses of a functionally graded transversely isotropic hollow cylinder that is presented in the elliptical coordinate system. The method of integral transform technique is used to produce an exact solution of the heat conduction equation in which sources are generated according to a linear function of the temperature. An explicit exact solution of the governing thermoelastic equation is proposed when material properties are power-law functions with the exponential form of the radial coordinate. Numerical calculations are also carried …

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Quasi-Linearization Method With Rational Legendre Collocation Method For Solving Mhd Flow Over A Stretching Sheet With Variable Thickness And Slip Velocity Which Embedded In A Porous Medium, M. M. Khader Dec 2018

Quasi-Linearization Method With Rational Legendre Collocation Method For Solving Mhd Flow Over A Stretching Sheet With Variable Thickness And Slip Velocity Which Embedded In A Porous Medium, M. M. Khader

Applications and Applied Mathematics: An International Journal (AAM)

The quasi-linearization method (QLM) and the rational Legendre functions are introduced here to present the numerical solution for the Newtonian fluid flow past an impermeable stretching sheet which embedded in a porous medium with a power-law surface velocity, variable thickness and slip velocity. Firstly, due to the high nonlinearity which yielded from the ordinary differential equation which describes the proposed physical problem, we construct a sequence of linear ODEs by using the QLM, hence the resulted equations become a system of linear algebraic equations. The comparison with the available results in the literature review proves that the obtained results via …

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Global Range Restricted Gmres For Linear Systems With Multiple Right Hand Sides, Mostafa Eslami Dec 2018

Global Range Restricted Gmres For Linear Systems With Multiple Right Hand Sides, Mostafa Eslami

Applications and Applied Mathematics: An International Journal (AAM)

This work concerns the solution of non-symmetric, sparse linear systems with multiple right hand sides by iterative methods. Herein a global version of the range restricted generalized minimal residual method (RRGMRES) is proposed for solving this sort of problems. Numerical results confirm that this new algorithm is applicable.

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Similarity Analysis Of Three Dimensional Nanofluid Flow By Deductive Group Theoretic Method, Hemangini Shukla, Hema C. Surati, M. G. Timol Dec 2018

Similarity Analysis Of Three Dimensional Nanofluid Flow By Deductive Group Theoretic Method, Hemangini Shukla, Hema C. Surati, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

The objective of this paper is to obtain similarity solution of three-dimensional nanofluid flow over flat surface stretched continuously in two lateral directions. Two independent variables from governing equations are reduced by applying deductive two parameter group theoretical method. Partial differential equations with boundary conditions are converted into ordinary differential equations with appropriate boundary conditions. Obtained equations are solved for temperature and velocity. The effect of nanoparticles volume fraction on temperature and velocity profile is investigated.

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Analysis Of Batch Arrival Bulk Service Queue With Multiple Vacation Closedown Essential And Optional Repair, G. Ayyappan, T. Deepa Dec 2018

Analysis Of Batch Arrival Bulk Service Queue With Multiple Vacation Closedown Essential And Optional Repair, G. Ayyappan, T. Deepa

Applications and Applied Mathematics: An International Journal (AAM)

The objective of this paper is to analyze an queueing model with multiple vacation, closedown, essential and optional repair. Whenever the queue size is less than , the server starts closedown and then goes to multiple vacation. This process continues until at least customer is waiting in the queue. Breakdown may occur with probability when the server is busy. After finishing a batch of service, if the server gets breakdown with a probability , the server will be sent for repair. After the completion of the first essential repair, the server is sent to the second optional repair with probability …

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On Chaplygin’S Method For First Order Neutral Differential Equation, Mamta Kumari, Y. S. Valaulikar Dec 2018

On Chaplygin’S Method For First Order Neutral Differential Equation, Mamta Kumari, Y. S. Valaulikar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we discuss the existence of a solution of a first order neutral differential equation with piecewise constant argument. We extend the method of Chaplygin’s sequence to obtain two sided bounds for the solution. These bounds are in the form of sequences of functions which are solutions of associated linear neutral differential equations with piecewise constant argument. This construction of monotonic sequences of upper and lower functions approximate, with increasing accuracy, the desired solution of the neutral differential equation with piecewise constant argument. Further we show that these sequences converge uniformly and monotonically to the unique solution of …

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Numerical Studies For Mhd Flow And Gradient Heat Transport Past A Stretching Sheet With Radiation And Heat Production Via Dtm, Khadijah M. Abualnaja Dec 2018

Numerical Studies For Mhd Flow And Gradient Heat Transport Past A Stretching Sheet With Radiation And Heat Production Via Dtm, Khadijah M. Abualnaja

Applications and Applied Mathematics: An International Journal (AAM)

This paper presents a numerically study for the effect of the internal heat generation, magnetic field and thermal radiation effects on the flow and gradient heat transfer of a Newtonian fluid over a stretching sheet. By using a similarity transformation, the governing PDEs can be transformed into a coupled non-linear system of ODEs with variable coefficients. Numerical solutions for these equations subject to appropriate boundary conditions are obtained by using the differential transformation method (DTM). The effects of various physical parameters such as viscosity parameter, the suction parameter, the radiation parameter, internal heat generation or absorption parameter and the Prandtl …

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Batch Arrival Bulk Service Queue With Unreliable Server, Second Optional Service, Two Different Vacations And Restricted Admissibility Policy, G. Ayyappan, R. Supraja Dec 2018

Batch Arrival Bulk Service Queue With Unreliable Server, Second Optional Service, Two Different Vacations And Restricted Admissibility Policy, G. Ayyappan, R. Supraja

Applications and Applied Mathematics: An International Journal (AAM)

This paper is concerned with batch arrival queue with an additional second optional service to a batch of customers with dissimilar service rate where the idea of restricted admissibility of arriving batch of customers is also introduced. The server may take two different vacations (i) Emergency vacation-during service the server may go for vacation to an emergency call and after completion of the vacation, the server continues the remaining service to a batch of customers. (ii) Bernoulli vacation-after completion of first essential or second optional service, the server may take a vacation or may remain in the system to serve …

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The Basins Of Convergence In The Planar Restricted Four-Body Problem With Variable Mass, Amit Mittal, Monika Arora, Md S. Suraj, Rajiv Aggarwal Dec 2018

The Basins Of Convergence In The Planar Restricted Four-Body Problem With Variable Mass, Amit Mittal, Monika Arora, Md S. Suraj, Rajiv Aggarwal

Applications and Applied Mathematics: An International Journal (AAM)

We have studied the existence, location and stability of the libration points in the model of restricted four-body problem (R4BP) with variable mass. It is assumed that three primaries, one dominant primary and the other two with equal masses, are always forming an equilateral triangle. We have determined the equations of motion of the above mentioned problem for the fourth body which is an infinitesimal mass. The libration points have been determined numerically for different values of the parameters considered. It is found that there are eight or ten libration points out of which six are non-collinear and two or …

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The Analysis Of M/M/1 Queue With Working Vacation In Fuzzy Environment, G. Kannadasan, N. Sathiyamoorth Dec 2018

The Analysis Of M/M/1 Queue With Working Vacation In Fuzzy Environment, G. Kannadasan, N. Sathiyamoorth

Applications and Applied Mathematics: An International Journal (AAM)

This study investigates the FM/FM/1 queue with working vacation. For this fuzzy queuing model, the researcher obtains some performance measure of interest such as the regular busy period, working vacation period, stationary queue length and waiting time. Finally, numerical results are presented to show the effects of system parameters.

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Stability Of Delayed Virus Infection Model With A General Incidence Rate And Adaptive Immune Response, Zhimin Chen, Xiuxiang Liu, Zhongzhong Xie Dec 2018

Stability Of Delayed Virus Infection Model With A General Incidence Rate And Adaptive Immune Response, Zhimin Chen, Xiuxiang Liu, Zhongzhong Xie

Applications and Applied Mathematics: An International Journal (AAM)

We present the dynamical behaviors of a virus infection model with general infection rate, immune responses and two intracellular delays which describe the interactions of the HIV virus, target cells, CTL cells and antibodies within host. Three factors are incorporated in this model: (1) the intrinsic growth rate of uninfected cells, (2) a nonlinear incidence rate function considering both virus-tocell infection and cell-to-cell transmission, and (3) a nonlinear productivity and removal function. By the method of Lyapunov functionals and LaSalle’s invariance principle, we show that the global dynamics of the model is determined by the reproductive numbers for viral infection …

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A De Casteljau Algorithm For Bernstein Type Polynomials Based On (P; Q)-Integers, Khalid Khan, D. K. Lobiyal, Adem Kilicman Dec 2018

A De Casteljau Algorithm For Bernstein Type Polynomials Based On (P; Q)-Integers, Khalid Khan, D. K. Lobiyal, Adem Kilicman

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a de Casteljau algorithm to compute (p; q)-Bernstein Bezier curves based on (p; q)- integers are introduced. The nature of degree elevation and degree reduction for (p; q)-Bezier Bernstein functions are studied. The new curves have some properties similar to q-Bezier curves. Moreover, we construct the corresponding tensor product surfaces over the rectangular domain (u; v) in [0; 1] x [0; 1] depending on four parameters. De Casteljau algorithm and degree evaluation properties of the surfaces for these generalization over the rectangular domain are investigated. Furthermore, some fundamental properties for (p; q)-Bernstein Bezier curves are discussed.We get …

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Analysis Of An Inventory Model With Time-Dependent Deterioration And Ramp-Type Demand Rate: Complete And Partial Backlogging, Vandana _ Dec 2018

Analysis Of An Inventory Model With Time-Dependent Deterioration And Ramp-Type Demand Rate: Complete And Partial Backlogging, Vandana _

Applications and Applied Mathematics: An International Journal (AAM)

The proposed model based on the global market strategies as for how the demand vary of the new seasonal products when they entered in the markets. The model has developed for the seasonal products or new consumer goods. The demand rate has considered Ramp-type based on the seasonal products having a time-dependent deterioration rate. The mathematical formulation of the proposed model is given. The present article consists two inventory model differ to each other as (a) in the first model stock-out situation is considered as completely backlogged; (b) in the second model partial backlogged stock-out situation is inserted. To obtain …

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Generalized Sylvester Polynomials Of In Several Variables, Nejla Özmen, Sule Soytürk Dec 2018

Generalized Sylvester Polynomials Of In Several Variables, Nejla Özmen, Sule Soytürk

Applications and Applied Mathematics: An International Journal (AAM)

This study deals with some new properties for the Generalized Sylvester polynomials in several variables. Some properties of these polynomials were given. We also derive an application giving certain families of bilateral generating functions for the Generalized Sylvester polynomials in several variables. At the end, we discuss some special cases.

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Numerical Treatment For The Flow Of Casson Fluid And Heat Transfer Model Over An Unsteady Stretching Surface In The Presence Of Internal Heat Generation/Absorption And Thermal Radiation, Mohammed M. Babatin Dec 2018

Numerical Treatment For The Flow Of Casson Fluid And Heat Transfer Model Over An Unsteady Stretching Surface In The Presence Of Internal Heat Generation/Absorption And Thermal Radiation, Mohammed M. Babatin

Applications and Applied Mathematics: An International Journal (AAM)

Several important industrial and engineering problems are very difficult to solve analytically since they are high nonlinear. The Chebyshev spectral collocation method possesses an ability to predict the solution behavior for a system of high nonlinear ordinary differential equations. This method which is based on differentiated Chebyshev polynomials is introduced to obtain an approximate solution to the system of ordinary differential equations which physically describe the flow and heat transfer problem of an unsteady Casson fluid model taking into consideration both heat generation and radiation effects in the temperature equation. Based on the spectral collocation method, the obtained solution is …

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Some Results On Lupaş (P; Q)-Bernstein Operators And Its Limit Form, Asif Khan, Vinita Sharma Dec 2018

Some Results On Lupaş (P; Q)-Bernstein Operators And Its Limit Form, Asif Khan, Vinita Sharma

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, statistical approximation properties of Lupaş (p; q)-analogue of Bernstein operators are studied. Rate of statistical convergence by means of modulus of continuity and Lipschitz type maximal functions has been investigated. Further Limit Lupaş (p; q)-Bernstein operators are defined and some results are investigated.

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Linear Stability Analysis With Solution Patterns Due To Varying Thermal Diffusivity For A Convective Flow In A Porous Medium, Dambaru Bhatta Dec 2018

Linear Stability Analysis With Solution Patterns Due To Varying Thermal Diffusivity For A Convective Flow In A Porous Medium, Dambaru Bhatta

Applications and Applied Mathematics: An International Journal (AAM)

Here we investigate the effect of the vertical rate of change in thermal diffusivity due to a hydrothermal convective flow in a horizontal porous medium. The continuity equation, the heat equation and the momentum-Darcy equation constitute the governing system for the flow in a porous medium. Assuming a vertically varying basic state, we derive the linear system and from this linear system, we compute the critical Rayleigh and wave numbers. Using fourth-order Runge-Kutta and shooting methods, we obtain the marginal stability curves and linear solutions to analyze the solution pattern for different diffusivity parameters.

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Study Of Transport Of Nanoparticles With K-L Model Through A Stenosed Microvessels, Rekha Bali, Nivedita Gupta Dec 2018

Study Of Transport Of Nanoparticles With K-L Model Through A Stenosed Microvessels, Rekha Bali, Nivedita Gupta

Applications and Applied Mathematics: An International Journal (AAM)

This paper studies a constitutive equation for blood with the transport of nanoparticles in a stenosed microvessel. The flow of blood through a bell-shaped stenosed micro blood vessel has been investigated with an importance of permeable walls that treats blood as non-Newtonian fluid by using K-L model. This model is more appropriate than other non-Newtonian models because K-L model involve three parameters such as plasma viscosity, yield stress and one other chemical variable while casson model involves only one parameter i.e. yield stress. In the present paper, the effective longitudinal diffusion of nanoparticles has been studied in stenosed blood vessel …

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Numerical Study Of Singular And Delta Shock Solutions Using A Large Time Step Method, Ilija Jegdic Dec 2018

Numerical Study Of Singular And Delta Shock Solutions Using A Large Time Step Method, Ilija Jegdic

Applications and Applied Mathematics: An International Journal (AAM)

We illustrate recently proposed large time step method for hyperbolic conservation laws. In the scalar case, it was proved earlier that if the approximate solutions converge boundedly, then they converge to the entropy solution. The main goal of this paper is to consider the large time step method for several systems of hyperbolic conservation laws. We compute approximate solutions to Riemann problems for three genuinely nonlinear one-dimensional systems (the Keyfitz-Kranzer system, the isentropic generalized Chaplygin gas dynamics equations, and the isentropic gas dynamics equations for polytropic gases with vanishing pressure). Besides approximating solutions that contain shocks and rarefaction waves, the …

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Simplifying Coefficients In A Family Of Ordinary Differential Equations Related To The Generating Function Of The Laguerre Polynomials, Feng Qi Dec 2018

Simplifying Coefficients In A Family Of Ordinary Differential Equations Related To The Generating Function Of The Laguerre Polynomials, Feng Qi

Applications and Applied Mathematics: An International Journal (AAM)

In the paper, by virtue of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the Lah inversion formula, the author simplifies coefficients in a family of ordinary differential equations related to the generating function of the Laguerre polynomials.

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