In this paper, a method based on modified adomian decomposition method for solving Seventh order integro-differential equations (MADM). The distinctive feature of the method is that it can be used to find the analytic solution without transformation of boundary value problems. To test the efficiency of the method presented two examples are solved by proposed method.

The aim of this paper is to propose a reliable iterative method for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibits that this technique was compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.

In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

This paper demonstrates a new technique based on a combined form of the new transform method with homotopy perturbation method to find the suitable accurate solution of autonomous Equations with initial condition.  This technique is called the transform homotopy perturbation method (THPM). It can be used to solve the problems without resorting to the frequency domain.The implementation of the suggested method demonstrates the usefulness in finding exact solution for linear and nonlinear problems. The practical results show the efficiency and reliability of technique and easier implemented than HPM in finding exact solutions.Finally, all algorithms in this paper implemented in MATLAB version 7.12.

   This paper applies the Modified Adomian Decomposition Method (MADM) for solving Integro-Differential Inequality, this method  is one of effective to construct analytic approximate solutions for linear and nonlinear integro-differential inequalities without solving many integrals and transformed or discretization. Several examples are presented, the analytic results show that this method is a promising and powerful for solving these problems.

This research aims to clarify the concept of doctrinal rules and adjust its basic terminologies. It further aims to lay down a map for the method of rooting this science by mentioning its rooted sources, in addition to drawing a miniature picture of its history, origin, formation and development. The paper ends with practical models to highlight its importance in rooting the science of nodal rules and facilitating the mentioning of its scattered discussions in a short and comprehensive phrase. The study further illustrates the pioneering role of doctrinal rules science in managing the doctrinal disputes, combining multiple sayings, and in bringing together opposing opinions. The study follows the inductive, descriptive and analytical app

     The aim of this paper is to study the nonlinear delay second order eigenvalue problems which consists of delay ordinary differential equations, in fact one of the expansion methods that is called the least square method which will be developed to solve this kind of problems.

Graphene-carbon nitride can be synthesized from thiourea in a single step at a temperature of four hours at a rate of 2.3 ℃/min. Graphene-carbon nitride was characterized by Fourier-transform infrared spectroscopy (FTIR), energy dispersive X-ray analysis (EDX), scanning electron microscopy, and spectrophotometry (UV-VIS). Graphene-carbon nitride was found to consist of triazine and heptazine structures, carbon, and nitrogen. The weight percentage of carbon and the atomic percentage of carbon are 40.08%, and the weight percentage of nitrogen and the atomic percentage of nitrogen are 40.08%. Therefore, the ratio and the dimensions of the graphene-carbon nitride were characterized by scanning electron microscopy, and it was found that the

Because of the quick growth of electrical instruments used in noxious gas detection, the importance of gas sensors has increased. X-ray diffraction (XRD) can be used to examine the crystal phase structure of sensing materials, which affects the properties of gas sensing. This contributes to the study of the effect of electrochemical synthesis of titanium dioxide (TiO₂) materials with various crystal phase shapes, such as rutile TiO₂ (R-TiO₂NTs) and anatase TiO₂ (A-TiO₂NTs). In this work, we have studied the effect of voltage on preparing TiO₂ nanotube arrays via the anodization technique for gas sensor applications. The results acquired from XRD, energy dispersion spectro

In this Paper, we proposed two new predictor corrector methods for solving Kepler's equation in hyperbolic case using quadrature formula which plays an important and significant rule in the evaluation of the integrals. The two procedures are developed that, in two or three iterations, solve the hyperbolic orbit equation in a very efficient manner, and to an accuracy that proves to be always better than 10-15. The solution is examined with and with grid size , using the first guesses hyperbolic eccentric anomaly is and , where is the eccentricity and is the hyperbolic mean anomaly.