فهرست مطالب maryam arabameri

One of the methods of solving multi-objective programming problems is the use of ideal programming problems, in which the decision maker considers an ideal level for each objective function. In real-life problems, several ideal levels may be available for an objective function, or these ideal levels are of fuzzy type, in which case fuzzy multi-choice ideal programming problems arise. In this article, the introduction and solution of fuzzy multi-choice ideal programming problems are discussed, so that first the problem becomes a fuzzy multi-choiceprogramming problem in which there are several choices for the right side of the constraints, then using fuzzy binarypolynomials and polynomials Fuzzy linear least squares is a classic linear programming problem, which is solved using Lingo software. The described algorithm is used to solve a practical example in the field of fuzzy multi-choice ideal programming problems, and the previous results are compared and analyzed with the results obtained from this method.

This article considers a particular type of fuzzy multi-choice linear programming (FMCLP) model in which there are several choices for the fuzzy parameters on the right-hand side (RHS) of problem constraints. We first construct the fuzzy polynomials to solve this model using the fuzzy multi-choice parameters on the RHS of constraints. We construct the fuzzy polynomials by approximating fuzzy functions, including the binary variable approach, Lagrange, and Newton's interpolating polynomials. Also, we use the least squares approach to construct the approximating fuzzy polynomial. Then we solve the resulting model. Finally, we will examine the above techniques in numerical examples.

In this paper, we are intend to present a numerical algorithm for computing approximate solution of linear and nonlinear Fredholm, Volterra and Fredholm-Volterra  integro-differential equations. The approximated solution is written in terms of fractional Jacobi polynomials. In this way, firstly we define Riemann-Liouville fractional operational matrix of fractional order Jacobi polynomials, then by using this matrix and the least squares method the solution of equation reduce to a system of algebraic equations which is solved through the Newton’s iterative method. In the next step we analyze convergence of the solution, and then to confirm the theoretical issue we examine some numerical examples. The results indicate the accuracy and efficiency of the method. The excellence of this method is its generality, which includes the fractional order Legendre and Chebyshev polynomials. Also it is also easy to use for linear and nonlinear integro-differential equations and provides good results.

This paper aims to advance the radial basis function method for solving space-time variable-order fractional partial differential equations. The fractional derivatives for time and space are considered in the Coimbra and the Riemann-Liouville sense, respectively. First, the time-variable fractional derivative is discretized through a finite difference approach. Then, the space-variable fractional derivative is approximated by radial basis functions. Also, we advance the Rippa algorithm to obtain a good value for the shape parameter of the radial basis functions. Results obtained from numerical experiments have been compared to the analytical solutions, which indicate high accuracy and efficiency for the proposed scheme.

In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the presented methods are efficient and applicable for lower and upper solutions.

In this paper, a moving mesh technique and a non-standard finite difference method are combined, and a moving mesh non-standard finite difference (MMNSFD) method is developed to solve an initial boundary value problem involving a quartic nonlinearity that arises in heat transfer with thermal radiation. In this method, the moving spatial grid is obtained by a simple geometric adaptive algorithm to preserve stability. Moreover, it uses variable time steps to protect the positivity condition of the solution. The results of this computational technique are compared with the corresponding uniform mesh non-standard finite difference scheme. The simulations show that the presented method is efficient and applicable, and approximates the solutions well, while because of producing unreal solution, the corresponding uniform mesh non-standard finite difference fails.

We introduce a RBFs mesheless method of lines that decomposes the interior and boundary centers to obtain the numerical solution of the time dependent PDEs. Then, the method is applied with an adaptive algorithm to obtain the numerical solution of one dimensional problem. We show that in the problems in which the solutions contain region with rapid variation, the adaptive RBFs methods are successful so that the PDE solution can be approximated well with a small number of basis functions. The method is described in detail, and computational experiments are performed for one-dimensional Burgers'' equations.

In this paper, we propose an adaptive mesh approach for time dependent parial differential equations, based on a so-called moving mesh PDE(MMPDE) and level set method. It means that the velocity of mesh nodes is calculated by MMPDE and is employed as veocity in the level set equation. Then, at each time level, the mesh points are considered as the level contours of the level set function. Finally the method is merged with local time step technique.