This paper investigates an effective computational method (ECM) based on the standard polynomials used to solve some nonlinear initial and boundary value problems appeared in engineering and applied sciences. Moreover, the effective computational methods in this paper were improved by suitable orthogonal base functions, especially the Chebyshev, Bernoulli, and Laguerre polynomials, to obtain novel approximate solutions for some nonlinear problems. These base functions enable the nonlinear problem to be effectively converted into a nonlinear algebraic system of equations, which are then solved using Mathematica®12. The improved effective computational methods (I-ECMs) have been implemented to solve three applications involving nonli

A relatively novel technique differential equations named Differential Transform Technique (DTM) is proposed. The evaluation of this approach is based on an iterative method in series form. Here, First give several basic definitions and properties of DTM, and applied various examples for the proposed method are tested to show the efficiency and accuracy to get the solutions of non-linear pantograph equation with elegantly computed components. In addition to solving the problems efficiently and rapidly, The advantage of the suggested approach is that it produces an analytical approach with fewer terms in a convergent series form.

An efficient combination of Adomian Decomposition iterative technique coupled with Laplace transformation to solve non-linear Random Integro differential equation (NRIDE) is introduced in a novel way to get an accurate analytical solution. This technique is an elegant combination of theLaplace transform, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (LT

In this paper we deal with the problem of ciphering and useful from group isomorphism for construct public key cipher system, Where construction 1-EL- Gamal Algorithm. 2- key- exchange Algorithm

An approach is depended in the recent years to distinguish any author or writer from other by analyzing his writings or essays. This is done by analyzing the syllables of writings of an author. The syllable is composed of two letters; therefore the words of the writing are fragmented to syllables and extract the most frequency syllables to become trait of that author. The research work depend on analyzed the frequency syllables in two cases, the first, when there is a space between the words, the second, when these spaces are ignored. The results is obtained from a program which scan the syllables in the text file, the performance is best in the first case since the sequence of the selected syllables is higher than the same syllables in

Electrospinning is a novel technique that can be used to produce highly porous fibers with highly tunable properties. In this research, this technique is adopted to prepare the electrospun nanofiber membrane for membrane distillation application. A custom-built electrospinning setup was made to prepare the nanofibers membrane. Polyvinylidene fluoride (PVDF) polymer was used in the electrospinning process due to its high hydrophobicity. Electrospun (PVDF) nanofibers were tested in direct contact membrane distillation (DCMD) process using 0.6 M sodium chloride as a feed solution. The resulting nanofiber membrane exhibited high performance in DCMD (i.e. relatively high water flux and high salt rejection). It has been found

      This work addressed the assignment problem (AP) based on fuzzy costs, where the objective, in this study, is to minimize the cost. A triangular, or trapezoidal, fuzzy numbers were assigned for each fuzzy cost. In addition, the assignment models were applied on linguistic variables which were initially converted to quantitative fuzzy data by using the Yager’sorankingi method. The paper results have showed that the quantitative date have a considerable effect when considered in fuzzy-mathematic models.