This paper devoted to the analysis of regular singular boundary value problems for ordinary differential equations with a singularity of the different kind , we propose semi - analytic technique using two point osculatory interpolation to construct polynomial solution, and discussion behavior of the solution in the neighborhood of the regular singular points and its numerical approximation. Many examples are presented to demonstrate the applicability and efficiency of the methods. Finally , we discuss behavior of the solution in the neighborhood of the singularity point which appears to perform satisfactorily for singular problems.

          In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

This paper introduces the Multistep Modified Reduced Differential Transform Method (MMRDTM). It is applied to approximate the solution for Nonlinear Schrodinger Equations (NLSEs) of power law nonlinearity. The proposed method has some advantages. An analytical approximation can be generated in a fast converging series by applying the proposed approach. On top of that, the number of computed terms is also significantly reduced. Compared to the RDTM, the nonlinear term in this method is replaced by related Adomian polynomials prior to the implementation of a multistep approach. As a consequence, only a smaller number of NLSE computed terms are required in the attained approximation. Moreover, the approximation also converges rapidly over a

The efficiency of internal combustion engines (ICE) is usually about thirty percent of the total energy of the fuel. The residual energy is lost in the exhaust gas, the lubrication, and the cooling water in the radiators. Recently much of the researcher’s efforts have focused on taking advantage of wasted energy of the exhaust gas. Using a thermoelectric generator (TEG) is one of the promising ways. However, TEG depends entirely on the temperature difference, which may be offered by the exhaust muffler. An experimental test has been conducted to study the thermal performance of a different muffler internal design. The researchers resort to the use of lost energy in an ICE using TEG, which is one of the ways to take adv

The assessment of data quality from different sources can be considered as a key challenge in supporting effective geospatial data integration and promoting collaboration in mapping projects. This paper presents a methodology for assessing positional and shape quality for authoritative large-scale data, such as Ordnance Survey (OS) UK data and General Directorate for Survey (GDS) Iraq data, and Volunteered Geographic Information (VGI), such as OpenStreetMap (OSM) data, with the intention of assessing possible integration. It is based on the measurement of discrepancies among the datasets, addressing positional accuracy and shape fidelity, using standard procedures and also directional statistics. Line feature comparison has been und

Air-conditioning systems (ACs) are essential in hot and humid climates to ensure acceptable ambient air quality as well as thermal comfort for buildings users. It is essential to improve refrigeration system performance without increasing the effects of global warming potential (GWP) and ozone depletion potential (ODP). The main objective of this study is to evaluate the performance of an air conditioning system that operates with a liquid suction heat exchanger (LSHX) through implementing refrigerants with zero OPD and low GWP (i.e., R134a and R1234yf). Liquid suction heat exchanger (LSHX) was added to an automobile air conditioning system (AACS).When Liquid suction heat exchanger was added to the cycle, primary results indicated t