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

This paper studies a novel technique based on the use of two effective methods like modified Laplace- variational method (MLVIM) and a new Variational method (MVIM)to solve PDEs with variable coefficients. The current modification for the (MLVIM) is based on coupling of the Variational method (VIM) and Laplace- method (LT). In our proposal there is no need to calculate Lagrange multiplier. We applied Laplace method to the problem .Furthermore, the nonlinear terms for this problem is solved using homotopy method (HPM). Some examples are taken to compare results between two methods and to verify the reliability of our present methods.

في هذا البحث، تم تنفيذ الطريقة الحسابية الفعالة (ECM) المستندة إلى متعددة الحدود القياسية الأحادية لحل مشكلة تدفق جيفري-هامل غير الخطية. علاوة على ذلك، تم تطوير واقتراح الطرق الحسابية الفعالة الجديدة في هذه الدراسة من خلال وظائف أساسية مناسبة وهي متعددات الحدود تشيبشيف، بيرنشتاين، ليجندر، هيرمت. يؤدي استخدام الدوال الأساسية إلى تحويل المسألة غير الخطية إلى نظام جبري غير خطي من المعادلات، والذي يتم حله بع

This paper presents a new transform method to solve partial differential equations, for finding suitable accurate solutions in a wider domain. It can be used to solve the problems without resorting to the frequency domain. The new transform is combined with the homotopy perturbation method in order to solve three dimensional second order partial differential equations with initial condition, and the convergence of the solution to the exact form is proved. The implementation of the suggested method demonstrates the usefulness in finding exact solutions. The practical implications show the effectiveness of approach and it is easily implemented in finding exact solutions.

       Finally, all algori

Scheduling Timetables for courses in the big departments in the universities is a very hard problem and is often be solved by many previous works although results are partially optimal. This work implements the principle of an evolutionary algorithm by using genetic theories to solve the timetabling problem to get a random and full optimal timetable with the ability to generate a multi-solution timetable for each stage in the collage. The major idea is to generate course timetables automatically while discovering the area of constraints to get an optimal and flexible schedule with no redundancy through the change of a viable course timetable. The main contribution in this work is indicated by increasing the flexibility of generating opti

Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

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

In this study, the performance of the adaptive optics (AO) system was analyzed through a numerical computer simulation implemented in MATLAB. Making a phase screen involved turning computer-generated random numbers into two-dimensional arrays of phase values on a sample point grid with matching statistics. Von Karman turbulence was created depending on the power spectral density. Several simulated point spread functions (PSFs) and modulation transfer functions (MTFs) for different values of the Fried coherent diameter (r_o) were used to show how rough the atmosphere was. To evaluate the effectiveness of the optical system (telescope), the Strehl ratio (S) was computed. The compensation procedure for an AO syst

The use of Bayesian approach has the promise of features indicative of regression analysis model classification tree to take advantage of the above information by, and ensemble trees for explanatory variables are all together and at every stage on the other. In addition to obtaining the subsequent information at each node in the construction of these classification tree. Although bayesian estimates is generally accurate, but it seems that the logistic model is still a good competitor in the field of binary responses through its flexibility and mathematical representation. So is the use of three research methods data processing is carried out, namely: logistic model, and model classification regression tree, and bayesian regression tree mode