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

       In this work, a solid core photonic crystal fibre (SC-PCF) has been designed with endlessly single mode of which both centerd core and holes in the cladding are organized by circles. The designed SC-PCF has a single solid centerd core which is ringed by a six rings hexagonal cladding. The computation of  SC-PCF is  achieved by using the finite element method (FEM) with perfectly matched layer (PML) boundary condition. All the designed factors like dimensions and distance of both core and cladding areas have varied with an optimized structure. After ending the numerical calculation, the results shows that there are a link between the air hols in the cladding ,  and the different normaliz

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

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

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

To evaluate and improve the efficiency of photovoltaic solar modules connected with linear pipes for water supply, a three-dimensional numerical simulation is created and simulated via commercial software (Ansys-Fluent). The optimization utilizes the principles of the 1st and 2nd laws of thermodynamics by employing the Response Surface Method (RSM). Various design parameters, including the coolant inlet velocity, tube diameter, panel dimensions, and solar radiation intensity, are systematically varied to investigate their impacts on energetic and exergitic efficiencies and destroyed exergy. The relationship between the design parameters and the system responses is validated through the development of a predictive model. Both single and mult

In this study, He's parallel numerical algorithm by neural network is applied to type of integration of fractional equations is Abel’s integral equations of the 1^st and 2^nd kinds. Using a Levenberge – Marquaradt training algorithm as a tool to train the network. To show the efficiency of the method, some type of Abel’s integral equations is solved as numerical examples. Numerical results show that the new method is very efficient problems with high accuracy.