In this paper, the proposed phase fitted and amplification fitted of the Runge-Kutta-Fehlberg method were derived on the basis of existing method of 4(5) order to solve ordinary differential equations with oscillatory solutions. The recent method has null phase-lag and zero dissipation properties. The phase-lag or dispersion error is the angle between the real solution and the approximate solution. While the dissipation is the distance of the numerical solution from the basic periodic solution. Many of problems are tested over a long interval, and the numerical results have shown that the present method is more precise than the 4(5) Runge-Kutta-Fehlberg method.

Experiments research is done to determine how saturated stiff clayey soil responds to a single impulsive load. Models made of saturated, stiff clay were investigated. To supply the single pulse energy, various falling weights from various heights were tested using the falling weight deflectometer (FWD). Dynamic effects can range from the major failure of a sensitive sensor or system to the apparent destruction of structures. This study examines the response of saturated stiff clay soil to a single impulsive load (vertical displacement at the soil surface below and beside the bearing plates). Such reactions consist of displacements, velocities, and accelerations caused by the impact occurring at the surface depth induced by the impact loads

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

Nonlinear time series analysis is one of the most complex problems ; especially the nonlinear autoregressive with exogenous variable (NARX) .Then ; the problem of model identification and the correct orders determination considered the most important problem in the analysis of time series . In this paper , we proposed splines  estimation method for model identification , then we used three criterions for the correct orders determination. Where ; proposed method used to estimate the additive splines for model identification , And the rank determination depends on the additive property  to avoid the problem of curse dimensionally . The proposed method is one of the nonparametric methods , and the simulation results give a

In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

This paper presents new modification of HPM to solve system of 3 rd order PDEs with initial condition, for finding suitable accurate solutions in a wider domain.

في هذا البحث نحاول تسليط الضوء على إحدى طرائق تقدير المعلمات الهيكلية لنماذج المعادلات الآنية الخطية والتي تزودنا بتقديرات متسقة تختلف أحيانا عن تلك التي نحصل عليها من أساليب الطرائق التقليدية الأخرى وفق الصيغة العامة لمقدرات K-CLASS. وهذه الطريقة تعرف بطريقة الإمكان الأعظم محدودة المعلومات "LIML" أو طريقة نسبة التباين الصغرى"LVR