INTERNATIONAL JOURNAL OF MATHEMATICAL MODELLING & COMPUTATION
Year:2014 | Volume:4 | Issue:1|Papers Count:8

A mathematical model for nutritional transport in capillary tissues exchange system in the presence of magnetic field has been studied. In this case, the cell is deformed. Due to concentration gradients, the dissolved nutrient in substrate diffuses into surrounding tissue. The analytical method is based on perturbation technique while the numerical simulation is based on finite difference scheme. Results concerning the concentration of dissolved nutrients, diffusive flux, normal component of velocity and skin friction coefficient, indicate that the presence of magnetic field influences the flow field considerably.

Using a generalized translation operator, we obtain a generalization of Theorem 5 in [4] for the Bessel transform for functions satisfying the (δ,g, 2)-Bessel Lipschitz condition in L2,a (R+).

In this paper, using the hyperbolic uniform spline of order 4 we develop the classes of methods for the numerical solution of second order boundary value problems (2VBP) with Dirichlet, Neumann and Cauchy types boundary conditions. The second derivativeis approximated by the three-point central difference scheme. The approximate results, obtained by the proposed method, confirm the convergence of numerical solutions. Numerical results are given to illustrate the efficiency of our methods.

Spectral approximations for ODEs in unbounded domains have only received limited attention. In many applicable problems, singular initial value problems arise. In solving these problems, most of numerical methods have difficulties and often could not pass the singular point successfully. In this paper, we apply the sinc-collocation method for solving singular initial value problems. The ability of the sinc-collocation method in overcoming the singular points difficulties makes it an efficient method in dealing with these equations. We use numerical examples to highlight efficiency of sinc-collocation method in problems with singularity in equations.

One of the most important issues in Data Envelopment Analysis (DEA) is sensitivity and stability region of a specific Decision Making Unit (DMU), including efficient and inefficient DMUs. In sensitivity analysis of efficient DMUs, the largest region should be found namely stability region that data variations are only for under e valuation efficient DMU and the data for the remaining DMUs are assumed fixed. Also under evaluation efficient DMU remains efficient with these variations. In sensitivity analysis of an inefficient DMU, it can obtain an efficiency score which is defined by the manager. In traditional DEA, we assume that all inputs and outputs are real amounts and consider continuous inputs and outputs. Although, there are some applications in which one or more inputs and/or outputs can only take integer quantities. In this paper, we obtain a stability region for efficient DMUs with integer data. Thus the inefficient DMU which is under evaluation can satisfy the decision maker and also it can be improved itself to gain a defined efficiency score by management, with integer data. The procedures are illustrated by numerical examples.

In this paper, we present a new iterative method with order of convergence sixth for solving nonlinear equations. This method is developed by extending a fourth order method of Ostrowski. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. A general error analysis providing the sixth order of convergence is given. Several numerical examples are given to illustrate the efficiency and performance of the new method.

In this paper we will present an adaptive wavelet scheme to solve the generalized Stokes problem. Using divergence free wavelets, the problem is transformed into an equivalent matrix vector system, that leads to a positive definite system of reduced size for the velocity. This system is solved iteratively, where the application of the infinite stiffness matrix, that is sufficiently compressible, is replaced by an adaptive approximation. Finally we prove that this adaptive method has optimal computational complexity, that is it recovers an approximate solution with desired accuracy at a computational expense that stays proportional to the number of terms in a corresponding wavelet-best N-term approximation.

In this paper, we give a numerical approach for approximating the solution of second kind Volterra integral equation with Logarithmic kernel using Block Pulse Functions (BPFs) and Taylor series expansion. Also, error analysis shows efficiency and applicability of the presented method. Finally, some numerical examples with exact solution are given.