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- Applications and Applied Mathematics: An International Journal (AAM) (173)
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Articles 1 - 30 of 199
Full-Text Articles in Applied Mathematics
(R2067) Solutions Of Hyperbolic System Of Time Fractional Partial Differential Equations For Heat Propagation, Sagar Sankeshwari, Vinayak Kulkarni
(R2067) Solutions Of Hyperbolic System Of Time Fractional Partial Differential Equations For Heat Propagation, Sagar Sankeshwari, Vinayak Kulkarni
Applications and Applied Mathematics: An International Journal (AAM)
Hyperbolic linear theory of heat propagation has been established in the framework of a Caputo time fractional order derivative. The solution of a system of integer and fractional order initial value problems is achieved by employing the Adomian decomposition approach. The obtained solution is in convergent infinite series form, demonstrating the method’s strengths in solving fractional differential equations. Moreover, the double Laplace transform method is employed to acquire the solution of a system of integer and fractional order boundary conditions in the Laplace domain. An inversion of double Laplace transforms has been achieved numerically by employing the Xiao algorithm in …
(R2074) A Comparative Study Of Two Novel Analytical Methods For Solving Time-Fractional Coupled Boussinesq-Burger Equation, Jyoti U. Yadav, Twinkle R. Singh
(R2074) A Comparative Study Of Two Novel Analytical Methods For Solving Time-Fractional Coupled Boussinesq-Burger Equation, Jyoti U. Yadav, Twinkle R. Singh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a comparative study between two different methods for solving nonlinear timefractional coupled Boussinesq-Burger equation is conducted. The techniques are denoted as the Natural Transform Decomposition Method (NTDM) and the Variational Iteration Transform Method (VITM). To showcase the efficacy and precision of the proposed approaches, a pair of different numerical examples are presented. The outcomes garnered indicate that both methods exhibit robustness and efficiency, yielding approximations of heightened accuracy and the solutions in a closed form. Nevertheless, the VITM boasts a distinct advantage over the NTDM by addressing nonlinear predicaments without recourse to the application of Adomian polynomials. …
(R2076) New Exact Solution Of Gilson–Pickering Equation In Plasma, Bingnuo Yang, Weinan Wu, Hongfeng Yu, Peng Guo
(R2076) New Exact Solution Of Gilson–Pickering Equation In Plasma, Bingnuo Yang, Weinan Wu, Hongfeng Yu, Peng Guo
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we use Paul-Painlev´e approach method, extended rational sine-cosine method and extended rational sinh-cosh method to construct the exact solution of the nonlinear Gilson-Pickering (GP) equation in plasma. The exact solution of GP equation obtained by the above three methods is new, and we use mathematical software to draw the two-dimensional and three-dimensional graphs of the new exact solutions. Through the study of nonlinear equations in plasma, this study will enrich the research and connotation of nonlinear development equations in plasma.
Entropy Analysis For Three-Dimensional Stretched Flow Of Viscous Fluid Engaging Radiation Effect And Double Diffusion Phenomenon, Syed Tehseen Abbas, Muhammad Sohail, Imran Haider
Entropy Analysis For Three-Dimensional Stretched Flow Of Viscous Fluid Engaging Radiation Effect And Double Diffusion Phenomenon, Syed Tehseen Abbas, Muhammad Sohail, Imran Haider
International Journal of Emerging Multidisciplinaries: Mathematics
A useful technique for comprehending the thermodynamic behavior of fluid flows is entropy analysis. In this paper, we explore the involvement and transfer of entropy in a stretched three-dimensional flow of a viscous fluid. The flow is presumed to be both laminar and incompressible, whereas the properties of the fluid are considered to be unchanged. The governing equations: continuity; momentum; and energy equations; are calculated using the necessary boundary conditions. Considering the acquired velocity and temperature profiles, the entropy generation rate and fluxes are calculated. The results demonstrate that entropy production is significantly influenced by the flow's stretching rate. Through …
Homotopy Perturbation Laplace Method For Boundary Value Problems, Mubashir Qayyum, Khadim Hussain
Homotopy Perturbation Laplace Method For Boundary Value Problems, Mubashir Qayyum, Khadim Hussain
International Journal of Emerging Multidisciplinaries: Mathematics
Most of the real situations are typically modeled as differential equations (DEs). Accurate solutions of such equations is one of the objective of researchers for the analysis and predictions in the physical systems. Typically, pure numerical approaches are utilized for the solution of such problems. These methods are usually consistent, but due to discretization and round-off errors, accuracy can be compromised. Also, pure numerical schemes may be computationally expensive and have large memory requirement. Due to this reason, current manuscript proposed a hybrid methodology by combining homotopy perturbation method (HPM) with Laplace transformation. This scheme provides excellent accuracy in less …
Effects Of Magnetic Field And Chemical Reaction On A Time Dependent Casson Fluid Flow, Akhil Mittal, Harshad Patel, Ramesh Patoliya, Vimalkumar Gohil
Effects Of Magnetic Field And Chemical Reaction On A Time Dependent Casson Fluid Flow, Akhil Mittal, Harshad Patel, Ramesh Patoliya, Vimalkumar Gohil
Applications and Applied Mathematics: An International Journal (AAM)
This research paper deals with the effect of chemical reactions and magnetic fields on the hydrodynamics fluid flow of Casson fluid. The novelty of this work is the inclusion of time-dependent flow across a vertical plate with a stepped concentration at the surface in a porous media. The stated phenomenon is modeled in the PDE system and is adapted in the ODE system through similarity transformation. The LT (Laplace Transform) and ILT (Inverse LT) are used to obtain the analytical results for regulating dimension-free movement, thermals, and concentration expression. The exact expression of shear rate, heat exchange rate, and mass …
Using A Sand Tank Groundwater Model To Investigate A Groundwater Flow Model, Christopher Evrard, Callie Johnson, Michael A. Karls, Nicole Regnier
Using A Sand Tank Groundwater Model To Investigate A Groundwater Flow Model, Christopher Evrard, Callie Johnson, Michael A. Karls, Nicole Regnier
CODEE Journal
A Sand Tank Groundwater Model is a tabletop physical model constructed of plexiglass and filled with sand that is typically used to illustrate how groundwater water flows through an aquifer, how water wells work, and the effects of contaminants introduced into an aquifer. Mathematically groundwater flow through an aquifer can be modeled with the heat equation. We will show how a Sand Tank Groundwater Model can be used to simulate groundwater flow through an aquifer with a no flow boundary condition.
(R2064) Analytical Approximations In Short Times Of Exact Operational Solutions To Reaction-Diffusion Problems On Bounded Intervals, Kwassi Anani
Applications and Applied Mathematics: An International Journal (AAM)
This paper aims to provide an exact solution in the Laplace domain and related analytic approximations in short time limits for the class of boundary value problems of the one-dimensional linear parabolic equation with constant coefficients. The problem’s most general form involves a parameterized equation on a bounded interval, with unified specification of the three classical types of boundary conditions: Dirichlet, Neumann, and Robin. Under certain integrability assumptions, we have proven that a unique solution exists in the Laplace domain. This operational solution can be obtained in a closed form by using classical integral transforms. Four distinct cases have been …
Computational Study Of Twin Circular Particles Settling In Fluid Using A Fictitious Boundary Approach, Imran Abbas, Kamran Usman
Computational Study Of Twin Circular Particles Settling In Fluid Using A Fictitious Boundary Approach, Imran Abbas, Kamran Usman
International Journal of Emerging Multidisciplinaries: Mathematics
The objective of this study is to examine the performance of two adjacent solid particles as they settle in close nearness, with a focus on comprehending the intricate interactions between the particles and the surrounding fluid during the process of sediment transport. Simulations are conducted with different initial horizontal spacing between particles and Reynolds numbers (Re). The findings of the simulations highlight the impact of the initial spacing between particles and Reynolds numbers (Re) as key factors influencing the ultimate settling velocity and separation distance. In general, when the initial spacing between particles is small and the Reynolds number (Re) …
On Solutions Of First Order Pde With Two-Dimensional Dirac Delta Forcing Terms, Ian Robinson
On Solutions Of First Order Pde With Two-Dimensional Dirac Delta Forcing Terms, Ian Robinson
Rose-Hulman Undergraduate Mathematics Journal
We provide solutions of a first order, linear partial differential equation of two variables where the nonhomogeneous term is a two-dimensional Dirac delta function. Our results are achieved by applying the unilateral Laplace Transform, solving the subsequently transformed PDE, and reverting back to the original space-time domain. A discussion of existence and uniqueness of solutions, a derivation of solutions of the PDE coupled with a boundary and initial condition, as well as a few worked examples are provided.
(R1966) Semi Analytical Approach To Study Mathematical Model Of Atmospheric Internal Waves Phenomenon, Patel Yogeshwari, Jayesh M. Dhodiya
(R1966) Semi Analytical Approach To Study Mathematical Model Of Atmospheric Internal Waves Phenomenon, Patel Yogeshwari, Jayesh M. Dhodiya
Applications and Applied Mathematics: An International Journal (AAM)
This research aims to study atmospheric internal waves which occur within the fluid rather than on the surface. The mathematical model of the shallow fluid hypothesis leads to a coupled nonlinear system of partial differential equations. In the shallow flow model, the primary assumption is that vertical size is smaller than horizontal size. This model can precisely replicate atmospheric internal waves because waves are dispersed over a vast horizontal area. A semi-analytical approach, namely modified differential transform, is applied successfully in this research. The proposed method obtains an approximate analytical solution in the form of convergent series without any linearization, …
(R2052) Flow Patterns For Newtonian And Non-Newtonian Fluids In A Cylindrical Pipe, Erick Sanchez, Dambaru Bhatta
(R2052) Flow Patterns For Newtonian And Non-Newtonian Fluids In A Cylindrical Pipe, Erick Sanchez, Dambaru Bhatta
Applications and Applied Mathematics: An International Journal (AAM)
A fully developed laminar steady flow of an incompressible, viscous fluid in a horizontal cylindrical pipe is considered here. Flow patterns for an incompressible, viscous fluid for both Newtonian and non-Newtonian fluids such as shear-thinning, shear-thickening and Bingham plastic fluids are analyzed in this study. Assuming that the flow is only due to the wall shear stress and the pressure drop, the velocity component in the axial direction for these cases is derived. Computational results of the velocity profiles for various cases are obtained using MATLAB and presented in graphical forms. It is observed that the velocity profile is parabolic …
(R2028) A Brief Note On Space Time Fractional Order Thermoelastic Response In A Layer, Navneet Lamba, Jyoti Verma, Kishor Deshmukh
(R2028) A Brief Note On Space Time Fractional Order Thermoelastic Response In A Layer, Navneet Lamba, Jyoti Verma, Kishor Deshmukh
Applications and Applied Mathematics: An International Journal (AAM)
In this study, a one-dimensional layer of a solid is used to investigate the exact analytical solution of the heat conduction equation with space-time fractional order derivatives and to analyze its associated thermoelastic response using a quasi-static approach. The assumed thermoelastic problem was subjected to certain initial and boundary conditions at the initial and final ends of the layer. The memory effects and long-range interaction were discussed with the help of the Caputo-type fractional-order derivative and finite Riesz fractional derivative. Laplace transform and Fourier transform techniques for spatial coordinates were used to investigate the solution of the temperature distribution and …
(R1885) Analytical And Numerical Solutions Of A Fractional-Order Mathematical Model Of Tumor Growth For Variable Killing Rate, N. Singha, C. Nahak
(R1885) Analytical And Numerical Solutions Of A Fractional-Order Mathematical Model Of Tumor Growth For Variable Killing Rate, N. Singha, C. Nahak
Applications and Applied Mathematics: An International Journal (AAM)
This work intends to analyze the dynamics of the most aggressive form of brain tumor, glioblastomas, by following a fractional calculus approach. In describing memory preserving models, the non-local fractional derivatives not only deliver enhanced results but also acknowledge new avenues to be further explored. We suggest a mathematical model of fractional-order Burgess equation for new research perspectives of gliomas, which shall be interesting for biomedical and mathematical researchers. We replace the classical derivative with a non-integer derivative and attempt to retrieve the classical solution as a particular case. The prime motive is to acquire both analytical and numerical solutions …
(R1894) Invariant Solution For Two-Dimensional And Axisymmetric Jet Of Power-Law Fluids, Bhavixa Bhagat, M. G. Timol
(R1894) Invariant Solution For Two-Dimensional And Axisymmetric Jet Of Power-Law Fluids, Bhavixa Bhagat, M. G. Timol
Applications and Applied Mathematics: An International Journal (AAM)
An invariant solution is derived using the Lie symmetry technique for steady laminar two-dimensional and axisymmetric boundary layer jet flow of incompressible power-law fluids with appropriate boundary conditions. Using symmetry, the nonlinear partial differential equation of the jet flow problem is transformed into a nonlinear ordinary differential equation. The resultant nonlinear ordinary differential equation with boundary conditions is converted to an initial value problem using the Lie symmetry technique. A numerical solution for the resulting initial value problem is derived using Fehlberg’s fourth-fifth order Runge-Kutta method through Maple software. The graphical representation of the characteristics of the velocity field for …
(R1969) On The Approximation Of Eventual Periodicity Of Linearized Kdv Type Equations Using Rbf-Ps Method, Hameed Ullah Jan, Marjan Uddin, Asma Norin, Tamheeda .
(R1969) On The Approximation Of Eventual Periodicity Of Linearized Kdv Type Equations Using Rbf-Ps Method, Hameed Ullah Jan, Marjan Uddin, Asma Norin, Tamheeda .
Applications and Applied Mathematics: An International Journal (AAM)
Water wave propagation phenomena still attract the interest of researchers from many areas and with various objectives. The dispersive equations, including a large body of classes, are widely used models for a great number of problems in the fields of physics, chemistry and biology. For instance, the Korteweg-de Vries (KdV) equation is one of the famous dispersive wave equation appeared in the theories of shallow water waves with the assumption of small wave-amplitude and large wave length, also its various modifications serve as the modeling equations in several physical problems. Another interesting qualitative characteristic of solutions of some dispersive wave …
(R2020) Dynamical Study And Optimal Harvesting Of A Two-Species Amensalism Model Incorporating Nonlinear Harvesting, Manoj Kumar Singh, Poonam .
(R2020) Dynamical Study And Optimal Harvesting Of A Two-Species Amensalism Model Incorporating Nonlinear Harvesting, Manoj Kumar Singh, Poonam .
Applications and Applied Mathematics: An International Journal (AAM)
This study proposes a two-species amensalism model with a cover to protect the first species from the second species, with the assumption that the growth of the second species is governed by nonlinear harvesting. Analytical and numerical analyses have both been done on this suggested ecological model. Boundedness and positivity of the solutions of the model are examined. The existence of feasible equilibrium points and their local stability have been discussed. In addition, the parametric conditions under which the proposed system is globally stable have been determined. It has also been shown, using the Sotomayor theorem, that under certain parametric …
(R1992) Rbf-Ps Method For Eventual Periodicity Of Generalized Kawahara Equation, Hameed Ullah Jan, Marjan Uddin, Arif Ullah, Naseeb Ullah
(R1992) Rbf-Ps Method For Eventual Periodicity Of Generalized Kawahara Equation, Hameed Ullah Jan, Marjan Uddin, Arif Ullah, Naseeb Ullah
Applications and Applied Mathematics: An International Journal (AAM)
In engineering and mathematical physics, nonlinear evolutionary equations play an important role. Kawahara equation is one of the famous nonlinear evolution equation appeared in the theories of shallow water waves possessing surface tension, capillary-gravity waves and also magneto-acoustic waves in a plasma. Another specific subjective parts of arrangements for some of evolution equations evidenced by findings link belonging to their long-term actions named as eventual time periodicity discovered over solutions to IBVPs (initial-boundary-value problems). Here we investigate the solution’s eventual periodicity for generalized fifth order Kawahara equation (IBVP) on bounded domain in combination with periodic boundary conditions numerically exploiting mesh-free …
(Si10-115) Controllability Results For Nonlinear Impulsive Functional Neutral Integrodifferential Equations In N-Dimensional Fuzzy Vector Space, Murugesan Nagarajan, Kumaran Karthik
(Si10-115) Controllability Results For Nonlinear Impulsive Functional Neutral Integrodifferential Equations In N-Dimensional Fuzzy Vector Space, Murugesan Nagarajan, Kumaran Karthik
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we concentrated to study the controllability of fuzzy solution for nonlinear impulsive functional neutral integrodifferential equations with nonlocal condition in n-dimensional vector space. Moreover, we obtained controllability of fuzzy result for the normal, convex, upper semi-continuous and compactly supported interval fuzzy number. Finally, an example was provided to reveal the application of the result.
(Si10-067) Numerical Study Of The Time Fractional Burgers’ Equation By Using Explicit And Implicit Schemes, Swapnali Doley, A. Vanav Kumar, L. Jino
(Si10-067) Numerical Study Of The Time Fractional Burgers’ Equation By Using Explicit And Implicit Schemes, Swapnali Doley, A. Vanav Kumar, L. Jino
Applications and Applied Mathematics: An International Journal (AAM)
The study discusses the numerical solution for a time fractional Burgers’ equation using explicit (scheme 1) and implicit scheme (scheme 2), respectively. The approximation of the differential equation is discretized using the finite difference method (FDM). A non-linear term present in the Burgers’ equation is approximated using the time-averaged values. The Von-Neumann analysis shows that the Scheme 1 is conditionally stable and Scheme 2 is unconditionally stable. The numerical solutions are compared with the exact solutions and are good in agreement. Also, the error is estimated between exact and numerical solutions.
Goursa Type Problem For A System Of Equations Of Poroelasticity, Kholmatzhon Imomnazarov, Lochin Khujayev, Zoyir Yangiboev
Goursa Type Problem For A System Of Equations Of Poroelasticity, Kholmatzhon Imomnazarov, Lochin Khujayev, Zoyir Yangiboev
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In this paper, in the description of the test process, we assume that the change in the temperature field of the environment will not affect the acoustic characteristics of the system are determined by the compressibility and viscosity of the fluid. Let us consider the effects caused by the shear modulus and coefficient of interfacial friction.
On The Consistency Of Alternative Finite Difference Schemes For The Heat Equation, Tran April
On The Consistency Of Alternative Finite Difference Schemes For The Heat Equation, Tran April
Rose-Hulman Undergraduate Mathematics Journal
While the well-researched Finite Difference Method (FDM) discretizes every independent variable into algebraic equations, Method of Lines discretizes all but one dimension, leaving an Ordinary Differential Equation (ODE) in the remaining dimension. That way, ODE's numerical methods can be applied to solve Partial Differential Equations (PDEs). In this project, Linear Multistep Methods and Method of Lines are used to numerically solve the heat equation. Specifically, the explicit Adams-Bashforth method and the implicit Backward Differentiation Formulas are implemented as Alternative Finite Difference Schemes. We also examine the consistency of these schemes.
Numerical Study Of Highly Efficient Centrifugal Cyclones, Murodil Madaliev
Numerical Study Of Highly Efficient Centrifugal Cyclones, Murodil Madaliev
Scientific-technical journal
Centrifugal cyclones have been developing for 100 years, while the efficiency of all cyclones for fine dust does not increase by 80%. The widespread use of cyclones in all branches of industrial production is determined by the simplicity of the design and sufficient reliability in operation. Along with this, the process carried out in a cyclone presents a complex scientific problem that has not been solved from the standpoint of aerohydromechanics. This is confirmed by various cyclone designs. Currently, the efficiency of cyclone cleaning of technological flows does not meet the requirements of sanitary standards and largely determines the level …
(R1491) Numerical Solution Of The Time-Space Fractional Diffusion Equation With Caputo Derivative In Time By A-Polynomial Method, Saeid Abbasbandy, Jalal Hajishafieiha
(R1491) Numerical Solution Of The Time-Space Fractional Diffusion Equation With Caputo Derivative In Time By A-Polynomial Method, Saeid Abbasbandy, Jalal Hajishafieiha
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a novel type of polynomial is defined which is equipped with an auxiliary parameter a. These polynomials are a combination of the Chebyshev polynomials of the second kind. The approximate solution of each equation is assumed as the sum of these polynomials and then, with the help of the collocation points, the unknown coefficients of each polynomial, as well as auxiliary parameter, is obtained optimally. Now, by placing the optimal value of a in polynomials, the polynomials are obtained without auxiliary parameter, which is the restarted step of the present method. The time discretization is performed …
(R1480) Heat Transfer In Peristaltic Motion Of Rabinowitsch Fluid In A Channel With Permeable Wall, Mahadev M. Channakote, Dilipkumar V. Kalse
(R1480) Heat Transfer In Peristaltic Motion Of Rabinowitsch Fluid In A Channel With Permeable Wall, Mahadev M. Channakote, Dilipkumar V. Kalse
Applications and Applied Mathematics: An International Journal (AAM)
This paper is intended to investigate the effect of heat transfer on the peristaltic flow of Rabinowitsch fluid in a channel lined with a porous material. The Navier -Stokes equation governs the channel's flow, and Darcy's law describes the permeable boundary. The Rabinowitsch fluid model's governing equations are solved by utilizing approximations of the long-wavelength and small number of Reynolds. The expressions for axial velocity, temperature distribution, pressure gradient, friction force, stream function are obtained. The influence on velocity, pressure gradient, friction force, and temperature on pumping action of different physical parameters is explored via graphs.
(R1496) Impact Of Electronic States Of Conical Shape Of Indium Arsenide/Gallium Arsenide Semiconductor Quantum Dots, Md. Fayz-Al-Asad, Md. Al-Rumman, Md. Nur Alam, Salma Parvin, Cemil Tunç
(R1496) Impact Of Electronic States Of Conical Shape Of Indium Arsenide/Gallium Arsenide Semiconductor Quantum Dots, Md. Fayz-Al-Asad, Md. Al-Rumman, Md. Nur Alam, Salma Parvin, Cemil Tunç
Applications and Applied Mathematics: An International Journal (AAM)
Semiconductor quantum dots (QDs) have unique atom-like properties. In this work, the electronic states of quantum dot grown on a GaAs substrate has been studied. The analytical expressions of electron wave function for cone-like quantum dot on the semiconductor surface has been obtained and the governing eigen value equation has been solved, thereby obtaining the dependence of ground state energy on radius and height of the cone-shaped -dots. In addition, the energy of eigenvalues is computed for various length and thickness of the wetting layer (WL). We discovered that the eigen functions and energies are nearly associated with the GaAs …
(R1494) Approximate Solutions Of The Telegraph Equation, Ilija Jegdić
(R1494) Approximate Solutions Of The Telegraph Equation, Ilija Jegdić
Applications and Applied Mathematics: An International Journal (AAM)
In this paper the initial boundary value problems for the linear telegraph equation in one and two space dimensions are considered. To find approximate solutions, a recently proposed optimization-free approach that utilizes artificial neural networks with one hidden layer is used, in which the connecting weights from the input layer to the hidden layer are chosen randomly and the weights from the hidden layer to the output layer are found by solving a system of linear equations. One of the advantages of this method, in comparison to the usual discretization methods for the two-dimensional linear telegraph equation, is that this …
Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria
Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria
Applications and Applied Mathematics: An International Journal (AAM)
The article aims to study a modified Leslie-Gower predator-prey model with Allee effect II, affecting the functional response with the assumption that the extent to which the environment provides protection to both predator and prey is the same. The model has been studied analytically as well as numerically, including stability and bifurcation analysis. Compared with the predator-prey model without Allee effect, it is found that the weak Allee effect II can bring rich and complicated dynamics, such as the model undergoes to a series of bifurcations (Homoclinic, Hopf, Saddle-node and Bogdanov-Takens). The existence of Hopf bifurcation has been shown for …
A High Order Finite Difference Method To Solve The Steady State Navier-Stokes Equations, Nihal J. Siriwardana, Saroj P. Pradhan
A High Order Finite Difference Method To Solve The Steady State Navier-Stokes Equations, Nihal J. Siriwardana, Saroj P. Pradhan
Applications and Applied Mathematics: An International Journal (AAM)
In this article, we develop a fourth order finite difference method to solve the system of steady state Navier-Stokes equations and apply it to the benchmark problem known as the square cavity flow problem. The numerical results of 𝑢-velocity components and 𝑣-velocity components obtained at the center of the cavity are compared with the results obtained by the method developed by Greenspan and Casulli to solve the time dependent system of Navier-Stokes equations. The method described in this article is easy to implement and it has been shown to be more efficient and stable than the method by Greenspan and …
Hybrid Algorithm For Singularly Perturbed Delay Parabolic Partial Differential Equations, Imiru T. Daba, Gemechis F. Duressa
Hybrid Algorithm For Singularly Perturbed Delay Parabolic Partial Differential Equations, Imiru T. Daba, Gemechis F. Duressa
Applications and Applied Mathematics: An International Journal (AAM)
This study aims at constructing a numerical scheme for solving singularly perturbed parabolic delay differential equations. Taylor’s series expansion is applied to approximate the shift term. The obtained result is approximated by using the implicit Euler method in the temporal discretization on a uniform step size with the hybrid numerical scheme consisting of the midpoint upwind method in the outer layer region and the cubic spline method in the inner layer region on a piecewise uniform Shishkin mesh in the spatial discretization. The constructed scheme is an ε−uniformly convergent accuracy of order one. Some test examples are considered to testify …