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Articles 211 - 236 of 236
Full-Text Articles in Numerical Analysis and Computation
On Numerical Solutions Of Two-Dimensional Boussinesq Equations By Using Adomian Decomposition And He's Homotopy Perturbation Method, Syed T. Mohyud-Din, Mustafa Inc, Ebru Cavlak
On Numerical Solutions Of Two-Dimensional Boussinesq Equations By Using Adomian Decomposition And He's Homotopy Perturbation Method, Syed T. Mohyud-Din, Mustafa Inc, Ebru Cavlak
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we obtain the approximate solution for 2-dimensional Boussinesq equation with initial condition by Adomian's decomposition and homotopy perturbation methods and numerical results are compared with exact solutions.
A Note On He’S Parameter-Expansion Method Of Coupled Van Der Pol–Duffing Oscillators, N. H. Sweilam, M. M. Khader
A Note On He’S Parameter-Expansion Method Of Coupled Van Der Pol–Duffing Oscillators, N. H. Sweilam, M. M. Khader
Applications and Applied Mathematics: An International Journal (AAM)
This paper presents the analytical and approximate solutions of the coupled chaotic Van der Pol-Duffing systems, by using the He's parameter-expansion method (PEM). One iteration is sufficient to obtain a highly accurate solution, which is valid for the whole solution domain. From the obtained results, we can conclude that the suggest method, is of utter simplicity, and can be easily extended to all kinds of non-linear equations.
Modified Variational Iteration Method For Second Order Initial Value Problems, Fazhan Geng
Modified Variational Iteration Method For Second Order Initial Value Problems, Fazhan Geng
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we introduce a modified variational iteration method for second order initial value problems by transforming the integral of iteration process. The main advantages of this modification are that it can overcome the restriction of the form of nonlinearity term in differential equations and improve the iterative speed of conventional variational iteration method. The method is applied to some nonlinear second order initial value problems and the numerical results reveal that the modified method is accurate and efficient for second order initial value problems.
Homotopy Perturbation Method And The Stagnation Point Flow, P. Donald Ariel
Homotopy Perturbation Method And The Stagnation Point Flow, P. Donald Ariel
Applications and Applied Mathematics: An International Journal (AAM)
The laminar steady flow of an incompressible, viscous fluid near a stagnation point has been computed using the homotopy perturbation method (HPM). Both the cases, (i) two-dimensional flow and (ii) axisymmetric flow, have been considered. A sequence of successive approximations has been obtained in the solution, and the convergence of the sequence is achieved by using the Padé approximants. It is found that there is a complete agreement between the results obtained by the HPM and the exact numerical solution.
Revised Variational Iteration Method For Solving Systems Of Ordinary Differential Equations, Elham Salehpoor, Hossein Jafari, Merieh A. Afrapoli
Revised Variational Iteration Method For Solving Systems Of Ordinary Differential Equations, Elham Salehpoor, Hossein Jafari, Merieh A. Afrapoli
Applications and Applied Mathematics: An International Journal (AAM)
A modification of the variational iteration method applied to systems of linear/non-linear ordinary differential equations, which yields a series solution with accelerated convergence, has been presented. Illustrative examples have been given.
Solutions Of Tenth And Ninth-Order Boundary Value Problems By Modified Variational Iteration Method, Syed Tauseef Mohyud-Din, Ahmet Yildirim
Solutions Of Tenth And Ninth-Order Boundary Value Problems By Modified Variational Iteration Method, Syed Tauseef Mohyud-Din, Ahmet Yildirim
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we apply the modified variational iteration method (MVIM) for solving the ninth and tenth-order boundary value problems. The proposed modification is made by introducing He’s polynomials in the correction functional. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed technique solves nonlinear problems without using the Adomian’s polynomials can be considered as a clear advantage of this algorithm …
Application Of Homotopy Analysis Method To Fourth-Order Parabolic Partial Differential Equations, M. Matinfar, M. Saeidy
Application Of Homotopy Analysis Method To Fourth-Order Parabolic Partial Differential Equations, M. Matinfar, M. Saeidy
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, by means of the homotopy analysis method (HAM), the solutions of some fourthorder parabolic partial differential equations are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter h that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear examples to obtain the exact solutions. The results reveal that the proposed method is very effective and simple.
Wavelet Transform Of Fractional Integrals For Integrable Boehmians, Deshna Loonker, P. K. Banerji, S. L. Kalla
Wavelet Transform Of Fractional Integrals For Integrable Boehmians, Deshna Loonker, P. K. Banerji, S. L. Kalla
Applications and Applied Mathematics: An International Journal (AAM)
The present paper deals with the wavelet transform of fractional integral operator (the Riemann- Liouville operators) on Boehmian spaces. By virtue of the existing relation between the wavelet transform and the Fourier transform, we obtained integrable Boehmians defined on the Boehmian space for the wavelet transform of fractional integrals.
Convergence Of The Sinc Method Applied To Volterra Integral Equations, M. Zarebnia, J. Rashidinia
Convergence Of The Sinc Method Applied To Volterra Integral Equations, M. Zarebnia, J. Rashidinia
Applications and Applied Mathematics: An International Journal (AAM)
A collocation procedure is developed for the linear and nonlinear Volterra integral equations, using the globally defined Sinc and auxiliary basis functions. We analytically show the exponential convergence of the Sinc collocation method for approximate solution of Volterra integral equations. Numerical examples are included to confirm applicability and justify rapid convergence of our method.
Approximations Of Sturm-Liouville Eigenvalues Using Sinc-Galerkin And Differential Transform Methods, Marwan Taiseer Alquran, Kamel Al-Khaled
Approximations Of Sturm-Liouville Eigenvalues Using Sinc-Galerkin And Differential Transform Methods, Marwan Taiseer Alquran, Kamel Al-Khaled
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we present a comparative study of Sinc-Galerkin method and differential transform method to solve Sturm-Liouville eigenvalue problem. As an application, a comparison between the two methods for various celebrated Sturm-Liouville problems are analyzed for their eigenvalues and solutions. The study outlines the significant features of the two methods. The results show that these methods are very efficient, and can be applied to a large class of problems. The comparison of the methods shows that although the numerical results of these methods are the same, differential transform method is much easier, and more efficient than the Sinc-Galerkin method.
Effects Of Radiation And Variable Viscosity On Mhd Free Convective Flow And Mass Transfer Over A Stretching Sheet With Chemical Reaction, M. A. Seddeek, A. A. Almushigeh
Effects Of Radiation And Variable Viscosity On Mhd Free Convective Flow And Mass Transfer Over A Stretching Sheet With Chemical Reaction, M. A. Seddeek, A. A. Almushigeh
Applications and Applied Mathematics: An International Journal (AAM)
A similarity solution is proposed for the analysis of steady free convection heat and mass transfer over a stretching sheet. The effect of radiation, chemical reaction and variable viscosity on hydromagnetic heat and mass transfer in the presence of magnetic field are investigated. The governing partial differential equations are transformed to the ordinary differential equations using similarity variables, and then solved numerically by means of the fourth-order Runge– Kutta method with shooting technique. A comparison with exact solution is performed and the results are found to be in excellent. Numerical results for the velocity, temperature and concentration as well as …
Higher Order Difference Schemes For Heat Equation, Jianzhong Wang
Higher Order Difference Schemes For Heat Equation, Jianzhong Wang
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we construct the explicit difference schemes for the heat equation with arbitrary high orders. We also show the validity of the new schemes by numerical simulations.
Variational Iteration Method For Solving Telegraph Equations, Syed T. Mohyud-Din, Muhammad A. Noor, Khalida I. Noor
Variational Iteration Method For Solving Telegraph Equations, Syed T. Mohyud-Din, Muhammad A. Noor, Khalida I. Noor
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we apply the variational iteration method (VIM) for solving telegraph equations, which arise in the propagation of electrical signals along a telegraph line. The suggested algorithm is more efficient and easier to handle as compare to the decomposition method. Numerical results show the efficiency and accuracy of the proposed VIM.
Circular Nonlinear Subdivision Schemes For Curve Design, Jian-Ao Lian, Yonghui Wang, Yonggao Yang
Circular Nonlinear Subdivision Schemes For Curve Design, Jian-Ao Lian, Yonghui Wang, Yonggao Yang
Applications and Applied Mathematics: An International Journal (AAM)
Two new families of nonlinear 3-point subdivision schemes for curve design are introduced. The first family is ternary interpolatory and the second family is binary approximation. All these new schemes are circular-invariant, meaning that new vertices are generated from local circles formed by three consecutive old vertices. As consequences of the nonlinear schemes, two new families of linear subdivision schemes for curve design are established. The 3-point linear binary schemes, which are corner-cutting depending on the choices of the tension parameter, are natural extensions of the Lane-Riesenfeld schemes. The four families of both nonlinear and linear subdivision schemes are implemented …
Transient Analysis Of Heat And Mass Transfer By Natural Convection In Power-Law Fluid Past A Vertical Plate Immersed In A Porous Medium (Numerical Study), Nasser S. Elgazery
Transient Analysis Of Heat And Mass Transfer By Natural Convection In Power-Law Fluid Past A Vertical Plate Immersed In A Porous Medium (Numerical Study), Nasser S. Elgazery
Applications and Applied Mathematics: An International Journal (AAM)
This paper attempted a numerical examination of the problem of unsteady free convection with heat and mass transfer from an isothermal vertical flat plate to a non-Newtonian fluid saturated porous medium. The flow in the porous medium was described via the Darcy-Brinkman-Forchheimer model. The simultaneous development of the problem of boundary layers was obtained numerically by finite difference method. Boundary layer and Boussinesq approximations had been incorporated. Numerical calculations were carried out for the various parameters entering into the problem. Velocity, temperature and concentration profiles were shown graphically and the physical quantities of the problem were given in tables. It …
Homotopy Perturbation Method And Padé Approximants For Solving Flierl-Petviashivili Equation, Syed T. Mohynd-Din, Muhammad A. Noor
Homotopy Perturbation Method And Padé Approximants For Solving Flierl-Petviashivili Equation, Syed T. Mohynd-Din, Muhammad A. Noor
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we present a reliable combination of homotopy perturbation method and Padé approximants to investigate the Flierl-Petviashivili (FP) equation. The approach introduces a new transformation necessary for the conversion of the Flierl-Petviashivili equation to a first order initial value problem and a reliable framework designed to overcome the difficulty of the singular point at x = 0. The proposed homotopy perturbation method is applied to the reformulated first order initial value problem which leads the solution in terms of transformed variable. The desired series solution is obtained by making use of the inverse transformation. The suggested algorithm may …
On A-Ary Subdivision For Curve Design Ii. 3-Point And 5-Point Interpolatory Schemes, Jian-Ao Lian
On A-Ary Subdivision For Curve Design Ii. 3-Point And 5-Point Interpolatory Schemes, Jian-Ao Lian
Applications and Applied Mathematics: An International Journal (AAM)
The a-ary 3-point and 5-point interpolatery subdivision schemes for curve design are introduced for arbitrary odd integer a greater than or equal to 3. These new schemes further extend the family of the classical 4- and 6-point interpolatory schemes.
A Reliable Approach For Higher-Order Integro-Differential Equations, Muhammad A. Noor, Syed T. Mohyud-Din
A Reliable Approach For Higher-Order Integro-Differential Equations, Muhammad A. Noor, Syed T. Mohyud-Din
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we apply the variational iteration method (VIM) for solving higher-order integro differential equations by converting the problems into system of integral equations. The proposed technique is applied to the re-formulated system of integro-differential equations. Numerical results show the accuracy and efficiency of the suggested algorithm. The fact that the VIM solves nonlinear problems without calculating Adomian’s polynomials is a clear advantage of this technique over the decomposition method.
Solving Higher Dimensional Initial Boundary Value Problems By Variational Iteration Decomposition Method, Muhammad A. Noor, Syed T. Mohyud-Din
Solving Higher Dimensional Initial Boundary Value Problems By Variational Iteration Decomposition Method, Muhammad A. Noor, Syed T. Mohyud-Din
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we apply a relatively new technique which is called the variational iteration decomposition method (VIDM) by combining the traditional variational iteration and the decomposition methods for solving higher dimensional initial boundary value problems. The proposed method is an elegant combination of variational iteration and the decomposition methods. The analytical results of the problems have been obtained in terms of convergent series with easily computable components. The method is quite efficient and is practically well suited for use in these problems. Several examples are given to verify the accuracy and efficiency of the proposed technique.
Chebyshev Collocation Method For The Effect Of Variable Thermal Conductivity On Micropolar Fluid Flow Over Vertical Cylinder With Variable Surface Temperature, Nasser S. Elgazery, Nader Y. Abd Elazem
Chebyshev Collocation Method For The Effect Of Variable Thermal Conductivity On Micropolar Fluid Flow Over Vertical Cylinder With Variable Surface Temperature, Nasser S. Elgazery, Nader Y. Abd Elazem
Applications and Applied Mathematics: An International Journal (AAM)
An analysis is performed to study the role of a variable thermal conductivity on unsteady free convection in a micro-polar fluid past a semi-infinite vertical cylinder with variable surface temperature in the presence of magnetic filed and radiation. The surface temperature is measured to vary as a power of the axial coordinate measured from the leading edge of the cylinder. The governing non-linear partial differential equations are transformed into a linear algebraic system utilizing Chebyshev collocation method in spatial and Crank-Nicolson method in time. Numerical results for the velocity, angular velocity and temperature profiles as well as for the local …
On A-Ary Subdivision For Curve Design: I. 4-Point And 6-Point Interpolatory Schemes, Jian-Ao Lian
On A-Ary Subdivision For Curve Design: I. 4-Point And 6-Point Interpolatory Schemes, Jian-Ao Lian
Applications and Applied Mathematics: An International Journal (AAM)
The classical binary 4-point and 6-point interpolatery subdivision schemes are generalized to a-ary setting for any integer a greater than or equal to 3. These new a-ary subdivision schemes for curve design are derived easily from their corresponding two-scale scaling functions, a notion from the context of wavelets.
Variational Iteration Method For Solving Initial And Boundary Value Problems Of Bratu-Type, Muhammad A. Noor, Syed T. Mohyud-Din
Variational Iteration Method For Solving Initial And Boundary Value Problems Of Bratu-Type, Muhammad A. Noor, Syed T. Mohyud-Din
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we present a reliable framework to solve the initial and boundary value problems of Bratu-type which are widely applicable in fuel ignition of the combustion theory and heat transfer. The algorithm rests mainly on a relatively new technique, the variational iteration method. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm.
Signed Decomposition Of Fully Fuzzy Linear Systems, Tofigh Allahviranloo, Nasser Mikaeilvand, Narsis A. Kiani, Rasol M. Shabestari
Signed Decomposition Of Fully Fuzzy Linear Systems, Tofigh Allahviranloo, Nasser Mikaeilvand, Narsis A. Kiani, Rasol M. Shabestari
Applications and Applied Mathematics: An International Journal (AAM)
System of linear equations is applied for solving many problems in various areas of applied sciences. Fuzzy methods constitute an important mathematical and computational tool for modeling real-world systems with uncertainties of parameters. In this paper, we discuss about fully fuzzy linear systems in the form AX = b (FFLS). A novel method for finding the non-zero fuzzy solutions of these systems is proposed. We suppose that all elements of coefficient matrix A are positive and we employ parametric form linear system. Finally, Numerical examples are presented to illustrate this approach and its results are compared with other methods.
Fuzzy Efficiency Measure With Fuzzy Production Possibility Set, T. Allahviranloo, F. Hosseinzade Lotfi, M. Adabitabar Firozja
Fuzzy Efficiency Measure With Fuzzy Production Possibility Set, T. Allahviranloo, F. Hosseinzade Lotfi, M. Adabitabar Firozja
Applications and Applied Mathematics: An International Journal (AAM)
The existing data envelopment analysis (DEA) models for measuring the relative efficiencies of a set of decision making units (DMUs) using various inputs to produce various outputs are limited to crisp data. The notion of fuzziness has been introduced to deal with imprecise data. Fuzzy DEA models are made more powerful for applications. This paper develops the measure of efficiencies in input oriented of DMUs by envelopment form in fuzzy production possibility set (FPPS) with constant return to scale.
Parameter Estimation In Nonlinear Coupled Advection-Diffusion Equation, Robert R. Ferdinand
Parameter Estimation In Nonlinear Coupled Advection-Diffusion Equation, Robert R. Ferdinand
Applications and Applied Mathematics: An International Journal (AAM)
In this paper a coupled system of two nonlinear advection-diffusion equations is presented. Such systems of equations have been used in mathematical literature to describe the dynamics of contaminant present in groundwater flowing through cracks in a porous rock matrix and getting absorbed into it. An inverse method procedure that approximates infinite-dimensional model parameters is described and convergence results for the parameter approximants are proved. This is finally followed by a computational experiment to compare theoretical and numerical results to verify accuracy of the mathematics analysis presented.
A Partially Discretized Age-Dependent Population Model With An Additional Stucture, Jean Tchuenche
A Partially Discretized Age-Dependent Population Model With An Additional Stucture, Jean Tchuenche
Applications and Applied Mathematics: An International Journal (AAM)
A semi-discretization method for solving an age-dependent population dynamics model with an additional structure is proposed. This method, unlike previous ones, considers the partial discretization which reduces the model equation into a first order ordinary differential equation. The latter is then solved explicitly and conditions under which second order accuracy arises are given. While the approach adopted is basically analytical, the main result shows that the sum of errors is bounded. An extension to the non-trivial case where growth depends on the additional parameter leads to a Riccati equation, and the existence and
convergence of solutions are proved.