In this work, an analytical approximation solution is presented, as well as a comparison of the Variational Iteration Adomian Decomposition Method (VIADM) and the Modified Sumudu Transform Adomian Decomposition Method (M STADM), both of which are capable of solving nonlinear partial differential equations (NPDEs) such as nonhomogeneous Kertewege-de Vries (kdv) problems and the nonlinear Klein-Gordon. The results demonstrate the solution’s dependability and excellent accuracy.

Metaheuristic is one of the most well-known fields of research used to find optimum solutions for non-deterministic polynomial hard (NP-hard) problems, for which it is difficult to find an optimal solution in a polynomial time. This paper introduces the metaheuristic-based algorithms and their classifications and non-deterministic polynomial hard problems. It also compares the performance of two metaheuristic-based algorithms (Elephant Herding Optimization algorithm and Tabu Search) to solve the Traveling Salesman Problem (TSP), which is one of the most known non-deterministic polynomial hard problems and widely used in the performance evaluations for different metaheuristics-based optimization algorithms. The experimental results of Ele

We consider some nonlinear partial differential equations in higher dimensions, the negative order of the Calogero-Bogoyavelnskii-Schiff (nCBS) equationin (2+1) dimensions, the combined of the Calogero-Bogoyavelnskii-Schiff equation and the negative order of the Calogero-Bogoyavelnskii-Schiff equation (CBS-nCBS) in (2+1) dimensions, and two models of the negative order Korteweg de Vries (nKdV) equations in (3+1) dimensions. We show that these equations can be reduced to the  same class of ordinary differential equations via wave reduction variable. Solutions in terms of symmetrical Fibonacci and Lucas functions are presented by implementation of the modified Kudryashov method.

In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

This paper presents a linear fractional programming problem (LFPP) with rough interval coefficients (RICs) in the objective function. It shows that the LFPP with RICs in the objective function can be converted into a linear programming problem (LPP) with RICs by using the variable transformations. To solve this problem, we will make two LPP with interval coefficients (ICs). Next, those four LPPs can be constructed under these assumptions; the LPPs can be solved by the classical simplex method and used with MS Excel Solver. There is also argumentation about solving this type of linear fractional optimization programming problem. The derived theory can be applied to several numerical examples with its details, but we show only two examples

In this paper, we develop the Hille and Nehari Type criteria for the oscillation of all solutions to the Fractional Differential Equations involving Conformable fractional derivative. Some new oscillatory criteria are obtained by using the Riccati transformations and comparison technique. We show the validity and effectiveness of our results by providing various examples.

This paper investigates some exact and local search methods to solve the traveling salesman problem. The Branch and Bound technique (BABT) is proposed, as an exact method, with two models. In addition, the classical Genetic Algorithm (GA) and Simulated Annealing (SA) are discussed and applied as local search methods. To improve the performance of GA we propose two kinds of improvements for GA; the first is called improved GA (IGA) and the second is Hybrid GA (HGA).

The IGA gives best results than GA and SA, while the HGA is the best local search method for all within a reasonable time for 5 ≤ n ≤ 2000, where n is the number of visited cities. An effective method of reducing the size of the TSP matrix was proposed with

In this search, a new pyrophosphate technique was proved. The technique was employed to single- nucleotide polymorphisms (SNPs), which diagnosis using a one-base extension reaction. Three Mycobacterium tuberculosis genes were chosen (Rpob, InhA, KatG) genes. Fifty-four specimens were used in this study fifty-three proved as drug-resistant specimens by The Iraqi Institute of Chest and Respiratory Diseases in Baghdad.; also one specimen was used as a negative control. The steps of this technique were by used a specific primer within each aliquot that has a short 3-OH end of the base of the target gene that was hybridized to the single-stranded DNA template. Then, the Taq polymerase enzyme and one of either α-thio-dATP, dTTP, dGTP, or dCTP

      The aim of this article is to present the exact analytical solution for models as system of (2+1) dimensional PDEs by using a reliable manner based on combined LA-transform with decomposition technique and the results have shown a high-precision, smooth and speed convergence to the exact solution compared with other classic methods. The suggested approach does not need any discretization of the domain or presents assumptions or neglect for a small parameter in the problem and does not need to convert the nonlinear terms into linear ones. The convergence of series solution has been shown with two illustrated examples such (2+1)D- Burger's system and (2+1)D- Boiti-Leon-Pempinelli (BLP) system.

In this paper, the effective computational method (ECM) based on the standard monomial polynomial has been implemented to solve the nonlinear Jeffery-Hamel flow problem. Moreover, novel effective computational methods have been developed and suggested in this study by suitable base functions, namely Chebyshev, Bernstein, Legendre, and Hermite polynomials. The utilization of the base functions converts the nonlinear problem to a nonlinear algebraic system of equations, which is then resolved using the Mathematica^®12 program. The development of effective computational methods (D-ECM) has been applied to solve the nonlinear Jeffery-Hamel flow problem, then a comparison between the methods has been shown. Furthermore, the maximum