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Articles 511 - 540 of 697
Full-Text Articles in Applied Mathematics
Stability Of Multiwavelet Frames With Different Matrix Dilations And Matrix Translations, F. A. Shah, Sunita Goyal
Stability Of Multiwavelet Frames With Different Matrix Dilations And Matrix Translations, F. A. Shah, Sunita Goyal
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we study the stability of multiwavelet frames with different matrix dilations and matrix translations by means of operator theory and show that these frames remain stable over some kinds of perturbations of the basic generators.
A Subdivision-Regularization Framework For Preventing Over Fitting Of Data By A Model, Ghulam Mustafa, Abdul Ghaffar, Muhammad Aslam
A Subdivision-Regularization Framework For Preventing Over Fitting Of Data By A Model, Ghulam Mustafa, Abdul Ghaffar, Muhammad Aslam
Applications and Applied Mathematics: An International Journal (AAM)
First, we explore the properties of families of odd-point odd-ary parametric approximating subdivision schemes. Then we fine-tune the parameters involved in the family of schemes to maximize the smoothness of the limit curve and error bounds for the distance between the limit curve and the kth level control polygon. After that, we present the subdivision-regularization framework for preventing over fitting of data by model. Demonstration shows that the proposed unified frame work can work well for both noise removal and overfitting prevention in subdivision as well as regularization.
An Ε -Uniform Numerical Method For A System Of Convection-Diffusion Equations With Discontinuous Convection Coefficients And Source Terms, T. Valanarasu, R. M. Priyadharshini, N. Ramanujam, A. Tamilselvan
An Ε -Uniform Numerical Method For A System Of Convection-Diffusion Equations With Discontinuous Convection Coefficients And Source Terms, T. Valanarasu, R. M. Priyadharshini, N. Ramanujam, A. Tamilselvan
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a parameter-uniform numerical method is suggested to solve a system of singularly perturbed convection-diffusion equations with discontinuous convection coefficients and source terms subject to the Dirichlet boundary condition. The second derivative of each equation is multiplied by a distinctly small parameter, which leads to an overlap and interacting interior layer. A numerical method based on a piecewise uniform Shishkin mesh is constructed. Numerical results are presented to support the theoretical results.
Solving Singularly Perturbed Differential Difference Equations Via Fitted Method, Awoke Andargie, Y. N. Reddy
Solving Singularly Perturbed Differential Difference Equations Via Fitted Method, Awoke Andargie, Y. N. Reddy
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we presented a fitted approach to solve singularly perturbed differential difference equations of second order with boundary at one end (left or right) of the interval. In this approach, with the help of Taylor series expansion, we approximated the terms containing negative and positive shifts and modified the singularly perturbed differential difference equation to singularly perturbed differential equation. A fitting parameter in the coefficient of the highest order derivative of the new equation is introduced and determined its value from the theory of singular perturbation. Finally, we obtained a three term recurrence relation which is solved using …
Physically-Realizable Uniform Temperature Boundary Condition Specification On A Wall Of An Enclosure: Part I – Problem Investigation, P. Y. C. Lee, W. H. Leong
Physically-Realizable Uniform Temperature Boundary Condition Specification On A Wall Of An Enclosure: Part I – Problem Investigation, P. Y. C. Lee, W. H. Leong
Applications and Applied Mathematics: An International Journal (AAM)
Designing an experimental apparatus requires considerable amount of planning. Despite proper planning, one can easily overlook a design such as the standard uniform temperature boundary condition applied to all or portion of a wall of an experimental apparatus. Although this boundary condition is mathematically simple and precise, achieving it physically may not be that simple. This paper addresses one such three-dimensional natural convection heat transfer apparatus that was designed to measure benchmark Nusselt numbers at various Rayleigh numbers with uniform temperatures specified at two walls of the enclosure. It was found that the effect of thermal spreading/constriction resistance on one …
Projected Surface Finite Elements For Elliptic Equations, Necibe Tuncer
Projected Surface Finite Elements For Elliptic Equations, Necibe Tuncer
Applications and Applied Mathematics: An International Journal (AAM)
In this article, we define a new finite element method for numerically approximating solutions of elliptic partial differential equations defined on “arbitrary” smooth surfaces S in RN+1. By “arbitrary” smooth surfaces, we mean surfaces that can be implicitly represented as level sets of smooth functions. The key idea is to first approximate the surface S by a polyhedral surface Sh, which is a union of planar triangles whose vertices lie on S; then to project Sh onto S. With this method, we can also approximate the eigenvalues and eigenfunctions of th Laplace-Beltrami operator on these “arbitrary” surfaces.
Physically-Realizable Uniform Temperature Boundary Condition Specification On A Wall Of An Enclosure: Part Ii – Problem Solution, P. Y. C. Lee, W. H. Leong
Physically-Realizable Uniform Temperature Boundary Condition Specification On A Wall Of An Enclosure: Part Ii – Problem Solution, P. Y. C. Lee, W. H. Leong
Applications and Applied Mathematics: An International Journal (AAM)
Temperature measurements along one side of the rectangular plate showed severe temperature non-uniformity along one side of a wall of a cubical experimental apparatus where the uniform temperature was physically desired. Despite proper planning and analyses, this non-uniformity was high enough that a benchmark study could not be carried out to the desired accuracy of about one percent error. This paper presents and extends analyses made previously based on the modifications to the original design of the apparatus to reduce the temperature non-uniformity on the wall by adding an auxiliary heater around a wall where the uniform temperature was desired. …
A New Implementation Of Gmres Using Generalized Purcell Method, Morteza Rahmani, Sayed H. Momeni-Masuleh
A New Implementation Of Gmres Using Generalized Purcell Method, Morteza Rahmani, Sayed H. Momeni-Masuleh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a new method based on the generalized Purcell method is proposed to solve the usual least-squares problem arising in the GMRES method. The theoretical aspects and computational results of the method are provided. For the popular iterative method GMRES, the decomposition matrices of the Hessenberg matrix is obtained by using a simple recursive relation instead of Givens rotations. The other advantages of the proposed method are low computational cost and no need for orthogonal decomposition of the Hessenberg matrix or pivoting. The comparisons for ill-conditioned sparse standard matrices are made. They show a good agreement with available …
Numerical Solution Of Some Nonlinear Volterra Integral Equations Of The First Kind, Leila Saeedi, Abolfazl Tari, Sayyed H. Momeni Masuleh
Numerical Solution Of Some Nonlinear Volterra Integral Equations Of The First Kind, Leila Saeedi, Abolfazl Tari, Sayyed H. Momeni Masuleh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the solving of a class of the nonlinear Volterra integral equations (NVIE) of the first kind is investigated. Here, we convert NVIE of the first kind to a linear equation of the second kind. Then we apply the operational Tau method to the problem and prove convergence of the presented method. Finally, some numerical examples are given to show the accuracy of the method.
Solutions Of System Of Fractional Partial Differential Equations, V. Parthiban, K. Balachandran
Solutions Of System Of Fractional Partial Differential Equations, V. Parthiban, K. Balachandran
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, system of fractional partial differential equation which has numerous applications in many fields of science is considered. Adomian decomposition method, a novel method is used to solve these type of equations. The solutions are derived in convergent series form which shows the effectiveness of the method for solving wide variety of fractional differential equations.
On The Geometrıc Interpretatıons Of The Kleın-Gordon Equatıon And Solution Of The Equation By Homotopy Perturbation Method, Hasan Bulut, H. M. Başkonuş
On The Geometrıc Interpretatıons Of The Kleın-Gordon Equatıon And Solution Of The Equation By Homotopy Perturbation Method, Hasan Bulut, H. M. Başkonuş
Applications and Applied Mathematics: An International Journal (AAM)
This paper is organized in the following ways: In the first part, we obtained the Klein Gordon Equation (KGE) in the Galilean space. In the second part, we applied Homotopy Perturbation Method (HPM) to this differential equation. In the third part, we gave two examples for the Klein Gordon equation. Finally, We compared the numerical results of this differential equation with their exact results. We also showed that approach used is easy and highly accurate.
Numerical Studies For Solving Fractional Riccati Differential Equation, N. H. Sweilam, M. M. Khader, A. M. S. Mahdy
Numerical Studies For Solving Fractional Riccati Differential Equation, N. H. Sweilam, M. M. Khader, A. M. S. Mahdy
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, finite difference method (FDM) and Pade'-variational iteration method (Pade'- VIM) are successfully implemented for solving the nonlinear fractional Riccati differential equation. The fractional derivative is described in the Caputo sense. The existence and the uniqueness of the proposed problem are given. The resulting nonlinear system of algebraic equations from FDM is solved by using Newton iteration method; moreover the condition of convergence is verified. The convergence's domain of the solution is improved and enlarged by Pade'-VIM technique. The results obtained by using FDM is compared with Pade'-VIM. It should be noted that the Pade'-VIM is preferable because …
On The Numerical Solution Of Linear Fredholm-Volterra İntegro Differential Difference Equations With Piecewise İntervals, Mustafa Gülsu, Yalçın Öztürk
On The Numerical Solution Of Linear Fredholm-Volterra İntegro Differential Difference Equations With Piecewise İntervals, Mustafa Gülsu, Yalçın Öztürk
Applications and Applied Mathematics: An International Journal (AAM)
The numerical solution of a mixed linear integro delay differential-difference equation with piecewise interval is presented using the Chebyshev collocation method. The aim of this article is to present an efficient numerical procedure for solving a mixed linear integro delay differential difference equations. Our method depends mainly on a Chebyshev expansion approach. This method transforms a mixed linear integro delay differential-difference equations and the given conditions into a matrix equation which corresponds to a system of linear algebraic equation. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer algebraic system …
Further Results On Fractional Calculus Of Saigo Operators, Praveen Agarwal
Further Results On Fractional Calculus Of Saigo Operators, Praveen Agarwal
Applications and Applied Mathematics: An International Journal (AAM)
A significantly large number of earlier works on the subject of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis (such as ordinary and partial differential equations, integral equations, special functions, summation of series, et cetera). The main object of the present paper is to study and develop the Saigo operators. First, we establish two results that give the image of the product of multivariable H-function and a general class of polynomials in Saigo operators. On account of the general nature of the Saigo operators, multivariable H-function and …
An Approximate Analytical Algorithm For Solving The Multispecies Lotka-Volterra Equations, Abdolsaeed Alavi, Asghar Ghorbani
An Approximate Analytical Algorithm For Solving The Multispecies Lotka-Volterra Equations, Abdolsaeed Alavi, Asghar Ghorbani
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a new efficient method called the parametric iteration method (PIM) is applied to accurately solve the multispecies Lotka–Volterra equations (MLVEs). Some cases of MLVEs are highlighted in order to show the simplicity and efficiency of the method. The results obtained in this work demonstrate that the present algorithm is a powerful analytic tool for the solution of MLVEs.
A Constructive Proof Of Fundamental Theory For Fuzzy Variable Linear Programming Problems, A. Ebrahimnejad
A Constructive Proof Of Fundamental Theory For Fuzzy Variable Linear Programming Problems, A. Ebrahimnejad
Applications and Applied Mathematics: An International Journal (AAM)
Two existing methods for solving fuzzy variable linear programming problems based on ranking functions are the fuzzy primal simplex method proposed by Mahdavi-Amiri et al. (2009) and the fuzzy dual simplex method proposed by Mahdavi-Amiri and Nasseri (2007). In this paper, we prove that in the absence of degeneracy these fuzzy methods stop in a finite number of iterations. Moreover, we generalize the fundamental theorem of linear programming in a crisp environment to a fuzzy one. Finally, we illustrate our proof using a numerical example.
Modification Of Truncated Expansion Method For Solving Some Important Nonlinear Partial Differential Equations, N. Taghizadeh, M. Mirzazadeh
Modification Of Truncated Expansion Method For Solving Some Important Nonlinear Partial Differential Equations, N. Taghizadeh, M. Mirzazadeh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we implemented modification of truncated expansion method for the exact solutions of the Konopelchenko-Dubrovsky equation the (n+1)-dimensional combined sinhcosh- Gordon equation and the Maccari system. Modification of truncated expansion method is a powerful solution method for obtaining exact solutions of nonlinear evolution equations. This method presents a wider applicability for handling nonlinear wave equations.
On Stability Of Dynamic Equations On Time Scales Via Dichotomic Maps, Veysel F. Hatipoğlu, Zeynep F. Koçak, Deniz Uçar
On Stability Of Dynamic Equations On Time Scales Via Dichotomic Maps, Veysel F. Hatipoğlu, Zeynep F. Koçak, Deniz Uçar
Applications and Applied Mathematics: An International Journal (AAM)
Dichotomic maps are used to check the stability of ordinary differential equations and difference equations. In this paper, this method is extended to dynamic equations on time scales; the stability and asymptotic stability to the trivial solution of the first order system of dynamic equations are examined using dichotomic and strictly dichotomic maps. This method, in dynamic equations, also involves Lyapunov’s direct method.
Two Reliable Methods For Solving The Modified Improved Kadomtsev-Petviashvili Equation, N. Taghizadeh, S. R. Moosavi Noori
Two Reliable Methods For Solving The Modified Improved Kadomtsev-Petviashvili Equation, N. Taghizadeh, S. R. Moosavi Noori
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, the tanh-coth method and the extended (G'/G)-expansion method are used to construct exact solutions of the nonlinear Modified Improved Kadomtsev-Petviashvili (MIKP) equation. These methods transform nonlinear partial differential equation to ordinary differential equation and can be applied to nonintegrable equation as well as integrable ones. It has been shown that the two methods are direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.
Investigation Of Nonlinear Problems Of Heat Conduction In Tapered Cooling Fins Via Symbolic Programming, Hooman Fatoorehchi, Hossein Abolghasemi
Investigation Of Nonlinear Problems Of Heat Conduction In Tapered Cooling Fins Via Symbolic Programming, Hooman Fatoorehchi, Hossein Abolghasemi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, symbolic programming is employed to handle a mathematical model representing conduction in heat dissipating fins with triangular profiles. As the first part of the analysis, the Modified Adomian Decomposition Method (MADM) is converted into a piece of computer code in MATLAB to seek solution for the mentioned problem with constant thermal conductivity (a linear problem). The results show that the proposed solution converges to the analytical solution rapidly. Afterwards, the code is extended to calculate Adomian polynomials and implemented to the similar, but more generalized, problem involving a power law dependence of thermal conductivity on temperature. The …
Applying Differential Transform Method To Nonlinear Partial Differential Equations: A Modified Approach, Marwan T. Alquran
Applying Differential Transform Method To Nonlinear Partial Differential Equations: A Modified Approach, Marwan T. Alquran
Applications and Applied Mathematics: An International Journal (AAM)
This paper proposes another use of the Differential transform method (DTM) in obtaining approximate solutions to nonlinear partial differential equations (PDEs). The idea here is that a PDE can be converted to an ordinary differential equation (ODE) upon using a wave variable, then applying the DTM to the resulting ODE. Three equations, namely, Benjamin-Bona-Mahony (BBM), Cahn-Hilliard equation and Gardner equation are considered in this study. The proposed method reduces the size of the numerical computations and use less rules than the usual DTM method used for multi-dimensional PDEs. The results show that this new approach gives very accurate solutions.
Distributional Properties Of Record Values Of The Ratio Of Independent Exponential And Gamma Random Variables, M. Shakil, M. Ahsanullah
Distributional Properties Of Record Values Of The Ratio Of Independent Exponential And Gamma Random Variables, M. Shakil, M. Ahsanullah
Applications and Applied Mathematics: An International Journal (AAM)
Both exponential and gamma distributions play pivotal roles in the study of records because of their wide applicability in the modeling and analysis of life time data in various fields of applied sciences. In this paper, a distribution of record values of the ratio of independent exponential and gamma random variables is presented. The expressions for the cumulative distribution functions, moments, hazard function and Shannon entropy have been derived. The maximum likelihood, method of moments and minimum variance linear unbiased estimators of the parameters, using record values and the expressions to calculate the best linear unbiased predictor of record values, …
Geometric Programming Subject To System Of Fuzzy Relation Inequalities, Elyas Shivanian, Mahdi Keshtkar, Esmaile Khorram
Geometric Programming Subject To System Of Fuzzy Relation Inequalities, Elyas Shivanian, Mahdi Keshtkar, Esmaile Khorram
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, an optimization model with geometric objective function is presented. Geometric programming is widely used; many objective functions in optimization problems can be analyzed by geometric programming. We often encounter these in resource allocation and structure optimization and technology management, etc. On the other hand, fuzzy relation equalities and inequalities are also used in many areas. We here present a geometric programming model with a monomial objective function subject to the fuzzy relation inequality constraints with maxproduct composition. Simplification operations have been given to accelerate the resolution of the problem by removing the components having no effect on …
A Mathematical Study On The Dynamics Of An Eco-Epidemiological Model In The Presence Of Delay, T. K. Kar, Prasanta K. Mondal
A Mathematical Study On The Dynamics Of An Eco-Epidemiological Model In The Presence Of Delay, T. K. Kar, Prasanta K. Mondal
Applications and Applied Mathematics: An International Journal (AAM)
In the present work a mathematical model of the prey-predator system with disease in the prey is proposed. The basic model is then modified by the introduction of time delay. The stability of the boundary and endemic equilibria are discussed. The stability and bifurcation analysis of the resulting delay differential equation model is studied and ranges of the delay inducing stability as well as the instability for the system are found. Using the normal form theory and center manifold argument, we derive the methodical formulae for determining the bifurcation direction and the stability of the bifurcating periodic solution. Some numerical …
Solving Singular Boundary Value Problems Using Daftardar-Jafari Method, H. Jafari, M. Ahmadi, S. Sadeghi
Solving Singular Boundary Value Problems Using Daftardar-Jafari Method, H. Jafari, M. Ahmadi, S. Sadeghi
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we apply the suggested iterative method by Daftardar and Jafari hereafter called Daftardar-Jafari method for solving singular boundary value problems. In the implementation of this new method, one does not need the computation of the derivative of the so-called Adomian polynomials. The method is quite efficient and is practically well suited for use in these problems. Two illustrative examples has been presented.
Boundary Stabilization Of Torsional Vibrations Of A Solar Panel, Prasanta K. Nandi, Ganesh C. Gorain, Samarjit Kar
Boundary Stabilization Of Torsional Vibrations Of A Solar Panel, Prasanta K. Nandi, Ganesh C. Gorain, Samarjit Kar
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we study a boundary stabilization of the torsional vibrations of a solar panel. The panel is held by a rigid hub at one end and is totally free at the other. The dynamics of the overall system leads to hybrid system of equations. It is set to a certain initial vibrations with a control torque as a stabilizer at the hub end only. Taking a non-linear damping as boundary stabilizer, a uniform exponential energy decay rate is obtained directly. Thus an explicit form of uniform stabilization of the system is achieved by means of the exponential energy …
Modeling And Analysis Of The Spread Of An Infectious Disease Cholera With Environmental Fluctuations, Manju Agarwal, Vinay Verma
Modeling And Analysis Of The Spread Of An Infectious Disease Cholera With Environmental Fluctuations, Manju Agarwal, Vinay Verma
Applications and Applied Mathematics: An International Journal (AAM)
A nonlinear delayed mathematical model with immigration for the spread of an infectious disease cholera with carriers in the environment is proposed and analyzed. It is assumed that all susceptible are affected by carrier population density. The carrier population density is assumed to follow the logistic model and grows due to conducive human population density related factors. The model is analyzed by stability theory of differential equations and computer simulation. Both the disease-free (DFE), (CFE) and endemic equilibria are found and their stability investigated. Bifurcation analyses about endemic equilibrium are also carried out analytically using the theory of differential equations. …
Introducing An Efficient Modification Of The Variational Iteration Method By Using Chebyshev Polynomials, M. M. Khader
Introducing An Efficient Modification Of The Variational Iteration Method By Using Chebyshev Polynomials, M. M. Khader
Applications and Applied Mathematics: An International Journal (AAM)
In this article an efficient modification of the variational iteration method (VIM) is presented using Chebyshev polynomials. Special attention is given to study the convergence of the proposed method. The new modification is tested for some examples to demonstrate reliability and efficiency of the proposed method. A comparison of our numerical results those of the conventional numerical method, the fourth-order Runge-Kutta method (RK4) are given. The comparison shows that the solution using our modification is fast-convergent and is in excellent conformance with the exact solution. Finally, we conclude that the proposed method can be applied to a large class of …
Distal Fuzzy Dynamical Systems, Y. Sayyari, M. R. Molaei
Distal Fuzzy Dynamical Systems, Y. Sayyari, M. R. Molaei
Applications and Applied Mathematics: An International Journal (AAM)
In this paper the t-distal notion is extended for fuzzy dynamical systems on fuzzy metric spaces. A method for constructing fuzzy metric spaces is studied. The product of t-distal fuzzy dynamical systems is considered. It is proved that: a product of fuzzy dynamical systems is t- distal if and only if its components are t-distal. The persistence of the t-distal property up to a fuzzy factor map is proved.
A New Four Point Circular-Invariant Corner-Cutting Subdivision For Curve Design, Jian-Ao Lian
A New Four Point Circular-Invariant Corner-Cutting Subdivision For Curve Design, Jian-Ao Lian
Applications and Applied Mathematics: An International Journal (AAM)
A 4-point nonlinear corner-cutting subdivision scheme is established. It is induced from a special C-shaped biarc circular spline structure. The scheme is circular-invariant and can be effectively applied to 2-dimensional (2D) data sets that are locally convex. The scheme is also extended adaptively to non-convex data. Explicit examples are demonstrated.