Nuran Guzel

A Fuzzy Set-Based Approach to Multi-objective Multi-item Solid Transportation Problem Under Uncertainty

In this paper, a multi-objective multi-item solid transportation problem (MOMISTP) with parameters, e.g., transportation costs, supplies, and demands, as trapezoidal fuzzy variables is formulated. In this MOMISTP, there are limitations on some items and conveyances so that some special items cannot be carried by means of some special conveyances. With the use of the nearest interval approximation of trapezoidal fuzzy numbers, an interval programming model is constructed for the fuzzy MOMISTP and then this model is turned into its deterministic form. Then, a new interval fuzzy programming approach is developed to obtain the optimal solution of the problem. Finally, a numerical example is presented for illustration.

On the numerical solution of stiff systems

Abstract In this paper, we use power series method to solve stiff ordinary differential equations of the first order and an ordinary differential equation of any order by converting it into a system of differential of the order one. Theoretical considerations has been discussed and some examples were presented to show the ability of the method for linear and nonlinear systems of differential equations. We use MAPLE computer algebra systems for numerical calculations [G. Frank, MAPLE V, CRC Press Inc., Florida, 1996].

Numerical solution of differential–algebraic equations with index-2

Abstract In this paper, numerical solution of differential–algebraic equations (DAEs) with index-2 has been presented using Pade approximation method. An index reduction for differential–algebraic equation with index-2 is suggested. First index-2 system is reduced to index-1 system. Then we have applied the method for solving differential–algebraic equations with index-2, numerically.

A Proposal to the Solution of Multiobjective Linear Fractional Programming Problem

We have proposed a new solution to the Multiobjective Linear Fractional Programming Problem (MOLFPP). The proposed solution is based on a theorem that deals with nonlinear fractional programming with single objective function and studied in the work by Dinkelbach, 1967. As a new contribution, we have proposed that is an efficient solution of MOLFPP if is an optimal solution of problem , where is for all . Hence, MOLFPP is simply reduced to linear programming problem (LPP). Some numerical examples are provided in order to illustrate the applications of the proposed method. The optimization software package, namely, WinQSB (Chang, 2001), has been employed in the computations.

Comparing Numerical Methods for Solving Time-Fractional Reaction-Diffusion Equations

Multivariate Pade approximation (MPA) is applied to numerically approximate the solutions of time-fractional reaction-diffusion equations, and the numerical results are compared with solutions obtained by the generalized differential transform method (GDTM). The fractional derivatives are described in the Caputo sense. Two illustrative examples are given to demonstrate the effectiveness of the multivariate Pade approximation (MPA). The results reveal that the multivariate Pade approximation (MPA) is very effective and convenient for solving time-fractional reaction-diffusion equations.

On the numerical solution of differential-algebraic equations with index-3

In this study, numerical solution of differential-algebraic equations (DAEs) with index-3 has been presented by Pade Approximation. An index reduction for differential-algebraic equation with index-3 is suggested. First index-3 system is reduced to index-1 system. Then we have applied the method for solving differential-algebraic equations with index-3 numerically.

Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

Two tecHniques were implemented, the Adomian decomposition method (ADM) and multivariate Pade approximation (MPA), for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM), then power series solution of fractional differential equation was put into multivariate Pade series. Finally, numerical results were compared and presented in tables and figures.