Non-linear equations are one of the most important and useful problems, which arises in a varied collection of practical applications in engineering and applied sciences. For this purpose, in this paper has been developed an iterative method with deprived of second derivative for the solution of non-linear problems. The developed deprived of second derivative iterative method is convergent quadratically, and which is derived from Newton Raphson Method and Taylor series. The numerical results of the developed method are compared with the Newton Raphson Method and Modified Newton Raphson Method. From graphical representation and numerical results, it has been observed that the deprived of second derivative iterative method is more appropriate and suitable as accuracy and iteration perception by the valuation of Newton Raphson Method and Modified Newton Raphson Method for estimating a non-linear problem.

The aim of this research article is to develop a three-step optimal iterative technique using Hermite interpolation for the solution of nonlinear algebraic and transcendental equation arises in chemical engineering models. In this connection, we proposed an optimal three-step eight-order technique without derivative and, has a high efficiency index. The convergence analysis of the proposed method is also discussed. For this demonstration, we apply the new technique to certain nonlinear problems in chemical engineering, such as, the conversion in a chemical reactor, a chemical equilibrium problem, azeotropic point of a binary solution and Continuous Stirred Tank Reactor (CSTR). And the study of dynamics is also used to demonstrate the performance of the presented scheme. It’s observed from the Comparison tables and dynamics, the proposed technique is more efficient compared to other existing methods.

The fundamental problem of linear algebra is to solve the system of linear equations (SOLE’s). To solve SOLE’s, is one of the most crucial topics in iterative methods. The SOLE’s occurs throughout the natural sciences, social sciences, engineering, medicine and business. For the most part, iterative methods are used for solving sparse SOLE’s. In this research, an improved iterative scheme namely, ‘’a new improved classical iterative algorithm (NICA)’’ has been developed. The proposed iterative method is valid when the co-efficient matrix of SOLE’s is strictly diagonally dominant (SDD), irreducibly diagonally dominant (IDD), M-matrix, Symmetric positive definite with some conditions and H-matrix. Such types of SOLE’s does arise usually from ordinary differential equations (ODE’s) and partial differential equations (PDE’s). The proposed method reduces the number of iterations, decreases spectral radius and increases the rate of convergence. Some numerical examples are utilized to demonstrate the effectiveness of NICA over Jacobi (J), Gauss Siedel (GS), Successive Over Relaxation (SOR), Refinement of Jacobi (RJ), Second Refinement of Jacobi (SRJ), Generalized Jacobi (GJ) and Refinement of Generalized Jacobi (RGJ) methods.

This study towards the Map-Matching process that is useful to align a location of Global Positioning System (GPS) of vehicles on the digital road networks. Today's GPS-enabled vehicles in developed countries generate a big volume of GPS data. On the other hand, the development of new roads in the city enables the road network very complex and difficult to match the vehicles' location. So therefore, different techniques (i.e., pre-processing techniques) may be applied before the map-matching process is a recent concern of the Intelligent Transport System (ITS) research community. In this paper, we introduce the pre-processing technique; splitting the road network graph and processing the Single Source Shortest Path (SSSP) in synchronize parallel processing in the Hadoop environment. The proposed technique enables the map-matching schemes efficient to align the GPS points on the digital road networks. In the experimental work, the results of the map-matching schemes (i.e., found in the literature review) incorporated with our proposed pre-processing technique shows better performance in aspect to the response time.

To solve the system of linear equations is one of the hottest topics in iterative methods. The system of linear equations occurs in business, engineering, social and in sensitive research areas like medicine, therefore applying efficient matrix solvers to such systems is crucial. In this paper, an improved iterative scheme using successive overrelaxation has been constructed. The proposed iterative method converges well when a linear system’s matrix is M-matrix, Symmetric positive definite with some conditions, irreducibly diagonally dominant, strictly diagonally dominant, and H-matrix. Such type of linear system of equations does arise usually from ordinary differential equations and partial differential equations. The improved iterative scheme has decreased spectral radius, improved stability and reduced the number of iterations. To show the effectiveness of the improved scheme, it is compared with the refinement of generalized successive over-relaxation and generalized successive over-relaxation method with the help of numerical experiments using MATLAB software.