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 is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

In this study, the flow and heat transfer characteristics of Al₂O₃-water nanofluids for a range of the Reynolds number of 3000, 4500, 6000 and 7500 with a range of volume concentration of 1%, 2%, 3% and 4% are studied numerically. The test rig consists of cold liquid loop, hot liquid loop and the test section which is counter flow double pipe heat exchanger with 1m length. The inner tube is made of smooth copper with diameter of 15mm. The outer tube is made of smooth copper with diameter of 50mm. The hot liquid flows through the outer tube and the cold liquid (or nanofluid) flow through the inner tube. The boundary condition of this study is thermally insulated the outer wall with uniform velocity a

This paper is dealing with non-polynomial spline functions "generalized spline" to find the approximate solution of linear Volterra integro-differential equations of the second kind and extension of this work to solve system of linear Volterra integro-differential equations. The performance of generalized spline functions are illustrated in test examples

Journal of Physics: Conference Series PAPER • THE FOLLOWING ARTICLE ISOPEN ACCESS Estimate the Rate of Contamination in Baghdad Soils By Using Numerical Method Luma Naji Mohammed Tawfiq1, Nadia H Al-Noor2 and Taghreed H Al-Noor1 Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series, Volume 1294, Issue 3 Citation Luma Naji Mohammed Tawfiq et al 2019 J. Phys.: Conf. Ser. 1294 032020 DOI 10.1088/1742-6596/1294/3/032020 DownloadArticle PDF References Download PDF 135 Total downloads 88 total citations on Dimensions. Turn on MathJax Share this article Share this content via email Share on Facebook (opens new window) Share on Twitter (opens new window) Share on Mendeley (opens new window) Hide article and author

The aim of this paper is to evaluate the rate of contamination in soils by using accurate numerical method as a suitable tool to evaluate the concentration of heavy metals in soil. In particular, 2D –interpolation methods are applied in the models of the spread the metals in different direction.The paper illustrates the importance of the numerical method in different applications, especially nvironment contamination. Basically, there are many roles for approximating functions. Thus, the approximating of function namely the analytical expression may be expressed; the most common type being is polynomials, which are the easy implemented and simplest methods of approximation. In this paper the divided difference formula is used and extended

Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained

A gliding arc discharge (GAD) with a water spray system was constructed. A non-thermal plasma, generated between two V shaped electrodes in an ambient argon driven by 100 Hz AC voltage, was investigated using optical emission spectroscopy (OES) with different gas flow rates (0.5, 1, 1.5, 2 , 2.5 , 3  1/min). Boltzmann plot method was used to calculate electron temperature (T_e) and electron density (n_e). The electrodes design was spectrally recognized and its T_e value was about 0.588-0.863 eV, while the n_e value of 6.875×10¹⁷-10.938×10¹⁷ cm^-3. The results of the plasma diagnostics generated by gliding arc showed that increasing gas f

The importance of kick tolerance in well operations has recently increased due to its implications in well design, in drilling and well control. To study a simple method for the application of kick tolerance concept in an effective way on the basis of field data, this research purpose is to improve knowledge about Kick Tolerance and represents a technical basis for the discussion on revision of standard procedure.

   The objective of this work is to review and to present a methodology of determination the kick tolerance parameters using the circulation kicks tolerance concepts.

   The proposed method allows to know, to evaluate and to analyze the kick tolerance problem in order to make the drilling exe

Been manufacturing detector Altosalih optical pattern contact metal semiconductor through deposition poles of aluminum metal on the chips of crystal cadmium Tleraad (CdTe) with directional [111] and growing with laboratory and annealed at a temperature 80c for 30 minutes and eat Study of some electrical properties nailed and scoutNmadj ??????? copper with non ??????? models to see effect Alichoab well research deals impact Alichoab and frequency detector resistance