فهرست مطالب
 Volume:10 Issue: 2, Spring 2022
 تاریخ انتشار: 1401/04/10
 تعداد عناوین: 12


Pages 173190
In this paper, an efficient finite difference method is presented for solving singularly perturbed linear second order parabolic problems with large time lag. The comparable numerical model is related to automatically controlled system with spatial diffusion of reactants in the processes. This study focuses on the formation of boundary layer behavior or oscillatory behaviors due to the presence of delay parameters and perturbation parameter. The numerical scheme comprising an exponentially fitted spline based difference scheme on a uniform mesh supported by CrankNicolson Method is constructed. It is found that the present method converges with second order accurate in both temporal and spatial variables. The convergence analysis and running time of the program with varied grid sizes are then used to do the efficiency analysis. The proposed scheme accuracy and efficiency are also demonstrated through numerical experiments.
Keywords: Singular perturbation, parabolic convectiondiffusion, large time delay, exponentially fitted method, parameter uniform convergence 
Pages 191201This paper is concerned with the existence of at least one positive solution for a boundary value problem (BVP), with $p$Laplacian, of the form begin{equation*} begin{split} (Phi_p(x^{'}))^{'} + g(t)f(t,x) &= 0, quad t in (0,1),\ x(0)ax^{'}(0) = alpha[x], & quad x(1)+bx^{'}(1) = beta[x], end{split} end{equation*}where $Phi_{p}(x) = x^{p2}x$ is a one dimensional $p$Laplacian operator with $p>1, a,b$ are real constants and $alpha,beta$ are the RiemannStieltjes integrals begin{equation*} begin{split} alpha[x] = int limits_{0}^{1} x(t)dA(t), quad beta[x] = int limits_{0}^{1} x(t)dB(t), end{split} end{equation*}with $A$ and $B$ are functions of bounded variation. A Homotopy version of Krasnosel'skii fixed point theorem is used to prove our results.Keywords: Fixed point, positive solution, $p$Laplacian, nonlocal boundary conditions, Boundary value problem

Pages 203212In the construction of efficient numerical methods for the stiff initial value problems, some second derivative multistep methods have been introduced equipping with super future point technique. In this paper, we are going to introduce a formula for the stability functions of a class of such methods. This group of methods encompasses SDBDF methods and their extensions with advanced steppoint feature. This general formula, instead of obtaining the distinct stability functions for each of methods, will facilitate stability analysis of the methods.Keywords: Initial value problem, second derivative methods, stability function, advancedstep point methods, stiff systems

Pages 213225
The problem of constructing a matrix by its spectral information is called inverse eigenvalue problem (IEP) which arises in a variety of applications. In this paper, we study an IEP for arrowhead matrices in different cases. The problem involves constructing of the matrix by some eigenvalues of each of the leading principal submatrices and one eigenpair. We will also investigate this problem and its variants in the cases of matrix entries being real, nonnegative, positive definite, complex and equal diagonal entries. To solve the problems, a new method to establish a relationship between the IEP and properties of symmetric and general form of matrices is developed. The necessary and sufficient conditions of the solvability of the problems are obtained. Finally, some numerical examples are presented.
Keywords: Inverse eigenvalue problem, Arrowhead matrix, Principal submatrix 
Pages 227245Data Envelopment Analysis (DEA) is a nonparametric method for measuring the relative efficiency of peer decisionmaking units (DMUs), where the internal structures of DMUs are treated as a black box. Traditional DEA models do not pay attention to the internal structures and intermediate values. Network data envelopment analysis models addressed this shortcoming by considering intermediate measure. The results of twostage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. The centralized model has been widely used to evaluate the efficiency of twostage systems, but the allocation problem of shared inputs and undesirable outputs has not been considered. The aim of this paper is to develop a method based on bargaining for evaluation in network DEA considering shared inputs and undesirable outputs. The two stages are considered as players to bargain for a better payoff, which is offered by DEA ratio efficiency score of DMUs. The efficiency model is developed as a cooperative game model. Finally, a numerical example is given to evaluate the proposed model.Keywords: Data envelopment analysis, Nash bargaining theory, shared inputs, twostage network, undesirable outputs

Pages 247261This paper provides a numerical solution for the fractional multicompartmental models which are applied in pharmacokinetics. We implement the local discontinuous Galerkin method for these fractional models with the upwind numerical fluxes. To obtain highorder results with adequate accuracy, the thirdorder approximation polynomials are used. Finally, to validate the scheme, the results are compared with the solutions of a semianalytical method.Keywords: Local discontinuous Galerkin method, Fractional compartmental model, Pharmacokinetics

Pages 263278In this paper, we tackle two important problems in lowrank learning, which are partial singular value decomposition and numerical rank estimation of huge matrices. By using the concepts of Krylov subspaces such as GolubKahan bidiagonalization (GKbidiagonalization) as well as Ritz vectors, we propose two methods for solving these problems in a fast and accurate way. Our experiments show the advantages of the proposed methods compared to the traditional and randomized singular value decomposition methods. The proposed methods are appropriate for applications involving huge matrices where the accuracy of the desired singular values and also all of their corresponding singular vectors are essential. As a real application, we evaluate the performance of our methods on the problem of Riemannian similarity learning between two different image datasets of MNIST and USPS.

Pages 279297This research describes a new fifthorder finite difference symmetrical WENOZ scheme for solving HamiltonJacobi equations. This method employs the same sixpoint stencil as the original fifthorder WENO scheme (SIAM J. Sci. Comput. 21 (2000) 21262143) and a new WENO scheme recently proposed (Numer. Methods Partial Differential Eq. 33 (2017) 10951113), and could generate better results and create the same order of accuracy in smooth area without loss of accuracy at critical points simultaneously avoiding incorrect oscillations in the vicinity of the singularities. The new reconstruction is a convex combination of a fifthorder linear reconstruction and three thirdorder linear reconstructions. We prepare a detailed analysis of the approximation order of the designed WENO scheme. Some benchmark tests in 1D, 2D and 3D are performed to display the capability of the scheme.Keywords: finite difference scheme, HamiltonJacobi equations, Symmetrical WENO, WENOZ scheme

Pages 299313In this paper, a waveletbased numerical algorithm is described to obtain approximate numerical solution of a class of nonlinear Fredholm integral equations of second kind having smooth kernels. The algorithm involves approximation of the unknown function in terms of Daubechies scale functions. The properties of Daubechies scale and wavelet functions together with onepoint quadrature rule for the product of a smooth function and Daubechies scale functions are utilized to transform the integral equation to a system of nonlinear equations. The efficiency of the proposed method is demonstrated through three illustrative examples.Keywords: Nonlinearity, Fredholm integral equation, Daubechies wavelet function, onepoint quadratute rule

Pages 315329
We study the combination of the Sinc and the Gaussian radial basis functions (GRBF) to develop the numerical methods for the timespace fractional diffusion equations with the Riesz fractional derivative. The GRBF is used to approximate the unknown function in spatial direction and the Sinc quadrature rule associated with double exponential transformation is applied to approximate the arising integrals. Three practical examples are considered for testing the ability of the proposed method.
Keywords: Fractional diffusion equations, Sinc method, double exponential transformation, Gaussian radial basis functions 
Pages 331348In this paper, the existence and the UlamHyers stability of solutions for the implicit secondorder differential equations are investigated via fractionalorders integral boundary conditions by direct application of the Banach contraction principle. Finally, we present some particular cases and two examples to illustrate our results.Keywords: Caputo fractional derivative, secondorder fractionalorder differential equation, Green's function, boundary value problems, nonlocal boundary conditions

Pages 349365The main target of this paper is to solve a system of twodimensional Volterra integral equations (2DVIEs). Operational Matrices of twodimensional hybrid of blockpulse functions and Legendre polynomials are applied to reduce these systems of integral equations to a system of algebraic equations. The main benefit of these basic functions is their efficiency in dealing with nonsufficiently smooth functions. An error bound is provided and some examples are prepared to verify the applicability of the offered numerical technique.Keywords: System of twodimensional Volterra integral equations, twodimensional hybrid functions, oroduct Operational matrix, operational matrices of integration