A new multi-criteria decision making method for the selection of construction contractors using interval valued fuzzy set.

OBJECTIVE: This article introduces a novel approach called Digital Weighted Multi Criteria Decision Making (DWMCDM) that employs interval valued fuzzy sets to select the best contractor for building projects. The contractor is chosen based on the pre-qualification and bid evaluation phases. In the first phase, the distance between the actual and required skills of the significant criteria is determined, and it is then converted into digital weighted distances to identify the maximum number of criteria related to the specific project of each contractor. The second step ranks the best contractor based on the bid price and digital weighted distances. RESULTS: The suggested technique integrates the pre-qualification and bid review phases to address project award delays and other restrictions. Finally, a real-world application is addressed to demonstrate the applicability of the proposed approach to any type of interval valued fuzzy inputs.

A derivative-free root-finding algorithm using exponential method and its implementation.

OBJECTIVE: In this paper, we develop a new root-finding algorithm to solve the given non-linear equations. The proposed root-finding algorithm is based on the exponential method. This algorithm is derivative-free and converges fast. RESULTS: Several numerical examples are presented to illustrate and validation of the proposed methods. Microsoft Excel and Maple implementation of the proposed algorithm is presented with sample computations.

On solving system of differential-algebraic equations using adomian decomposition method.

Background: In this paper, we focus on an efficient and easy method for solving the given system of differential-algebraic equations (DAEs) of second order. Methods: The approximate solutions are computed rapidly and efficiently with the help of a semi-analytical method known as Adomian decomposition method (ADM). The logic of this method is simple and straightforward to understand. Results: To demonstrate the proposed method, we presented several examples and the computations are compared with the exact solutions to show the efficient. One can employ this logic to different mathematical software tools such as Maple, SCILab, Mathematica, NCAlgebra, Matlab etc. for the problems in real life applications. Conclusions: In this paper, we offered a method for solving the given system of secondorder nonlinear DAEs with aid of the ADM. We shown that the proposed method is simple and efficient, also one can obtain the approximate solutions quickly using this method. A couple of examples are discussed for illustrating this method and graphical and mathematical assessments are discussed with the analytical solutions of the given problems.

On new sixth and seventh order iterative methods for solving non-linear equations using homotopy perturbation technique.

OBJECTIVES: This paper proposes three iterative methods of order three, six and seven respectively for solving non-linear equations using the modified homotopy perturbation technique coupled with system of equations. This paper also discusses the analysis of convergence of the proposed iterative methods. RESULTS: Several numerical examples are presented to illustrate and validation of the proposed methods. Implementation of the proposed methods in Maple is discussed with sample computations.

On solving initial value problems for partial differential equations in maple.

OBJECTIVES: In this paper, we present and employ symbolic Maple software algorithm for solving initial value problems (IVPs) of partial differential equations (PDEs). From the literature, the proposed algorithm exhibited a great significant in solving partial differential equation arises in applied sciences and engineering. RESULTS: The implementation include computing partial differential operator (PartialDiffOperator), Greens function (GreensFunction) and exact solution (ExactSolution) of the given IVP. We also present syntax, ApplyPartialDiffOp, to apply the partial differential operator to verify the solution of the given IVP obtained from ExactSolution. Sample computations are presented to illustrate the maple implementation.

Quadratically convergent algorithm for computing real root of non-linear transcendental equations.

OBJECTIVES: The present paper describes a new algorithm to find a root of non-linear transcendental equations. It is found that Regula-Falsi method always gives guaranteed result but slow convergence. However, Newton-Raphson method does not give guaranteed result but faster than Regula-Falsi method. Therefore, the present paper used these two ideas and developed a new algorithm which has better convergence than Regula-Falsi and guaranteed result. One of the major issue in Newton-Raphson method is, it fails when first derivative is zero or approximately zero. RESULTS: The proposed method implemented the failure condition of Newton-Raphson method with better convergence. Error calculation has been discussed for certain real life examples using Bisection, Regula-Falsi, Newton-Raphson method and new proposed method. The computed results show that the new proposed quadratically convergent method provides better convergence than other methods.

Initial value problems for system of differential-algebraic equations in Maple.

OBJECTIVES: In this paper, we discuss a Maple package, deaSolve, of the symbolic algorithm for solving an initial value problem for the system of linear differential-algebraic equations with constant coefficients. RESULTS: Using the proposed Maple package, one can compute the desired Green's function of a given IVP. Sample computations are presented to illustrate the Maple package.