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The operational matrices for Elliptic Partial Differential Equations with mixed boundary conditions
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Abstract<p>The purpose of this research is to implement the orthogonal polynomials associated with operational matrices to get the approximate solutions for solving two-dimensional elliptic partial differential equations (E-PDEs) with mixed boundary conditions. The orthogonal polynomials are based on the Standard polynomial (<italic>x<sup>i</sup> </italic>), Legendre, Chebyshev, Bernoulli, Boubaker, and Genocchi polynomials. This study focuses on constructing quick and precise analytic approximations using a simple, elegant, and potent technique based on an orthogonal polynomial representation of the solution as a double power series. Consequently, a linear partial differential equation is transformed into a linear algebraic system which is solved by the Mathematica®12. Approximate solutions can be found if the answers are polynomials in and of itself. Three applications involving well-known linear problems Laplace, Poisson, and Helmholtz equations have been solved by using the proposed methods, and a comparison of the approaches has been provided. Furthermore, the computation of the error norm <italic>L<sub>∞</sub> </italic> has been done to show the accuracy of the suggested approaches. The results clearly demonstrate how precise, efficient, and dependable the proposed methods are in obtaining rough solutions to the problem. Bernoulli was one of the best methods in most examples.</p>
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Publication Date
Thu Sep 01 2016
Journal Name
Journal Of Engineering
Effect of Using Porcelanite as Partial Replacement of Fine Aggregate on Roller Compacted Concrete with Different Curing Methods
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Roller-Compacted Concrete is a no-slump concrete, with no reinforcing steel, no forms, no finishing and wet enough to support compaction by vibratory rollers. Due to the effect of curing on properties and durability of concrete, the main purpose of this research is to study the effect of various curing methods (air curing, 7 days water curing, and permanent water curing) and porcelanite (local material used as an Internal Curing agent) with different replacement percentages of fine aggregate (volumetric replacement) on some properties of Roller-Compacted Concrete and to explore the possibility of introducing practical Roller-Compacted Concrete for road pavement with minimum requirement of curing. Specimens were sawed fro

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Publication Date
Thu Aug 15 2013
Journal Name
Journal Of The College Of Basic Education
Synthesis and Characterization Mixed Ligands of Phenylalanine and Tributylphosphine Complexes with Selected Metal Ions.
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Complexes of Co(II),Ni(II),Cu(II) and Zn(II) with mixed ligands of phenylalanine (L) and tributylphosphine (TBPh) were prepared in aqueous ethanol with (2:1:1) (M:L:TBPh). The prepared complexes were characterized using flame atomic absorption,(C.H.N)Analysis, FT.IR and UV-Vis spectroscopic methods as well as magnetic susceptibility and conductivity measurements. In addition biological activity of the phenylalanine and complexes against two selected type of bacteria were also examined. Some of the complexes exhibit good bacterial activities. From the obtained data the octahedral structure was suggested for all prepared complexes.

Publication Date
Sun Oct 01 2017
Journal Name
International Journal Of Science And Research
Synthesis, Spectroscopic Studies and Biologically Active of Uracil and Mixed Ligand with Aluminum (III)
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New complexes of Al(III) such as [Al (Ura) (Phen) (OH2) Cl ] Cl. 2H2O, [Al(Ura)2(OA)(OH2)Cl].H2O and [Al(Ura)3Cl3]H2O type, where (Ura)=Uracil, (Phen)= 1,10-Phenanthroline monohydrate and (OA)= Oxalic acid dihydrate, were prepared. The elemental microanalysis, FT.IR, electronic spectra, and magnetic susceptibility as well as the conductivity measurements are characterized. For isolated three complexes for six coordinated of Al(III) are proposed with molecular formulas that depend on the nature of (Ura), (Phen) and (OA) present. The suggested molecular structure into all complexes for aluminum ion is octahedral geometries .The antibacterial efficacy was examined from metal salt (AlCl3), ligands and metal complexes into the pathogenic bacteri

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Publication Date
Sat Oct 01 2011
Journal Name
Journal Of Engineering
DEVELOPING LAMINAR MIXED CONVECTION HEAT TRANSFER THROUGH VERTICAL CONCENTRIC ANNULI WITH ADIABATIC INNER CYLINDER
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Theoretical and experimental investigations have been carried out on developing laminar
combined free and forced convection heat transfer in a vertical concentric annulus with uniformly
heated outer cylinder (constant heat flux) and adiabatic inner cylinder for both aiding and opposing
flows. The theoretical investigation involved a mathematical modeling and numerical solution for
two dimensional, symmetric, simultaneously developing laminar air flows was achieved. The
governing equations of motion (continuity, momentum and energy) are solved by using implicit
finite difference method and the Gauss elimination technique. The theoretical work covers heat flux
range from (200 to 1500) W/m2, Re range from 400 to 2000 an

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Publication Date
Thu Jan 08 2026
Journal Name
Heat Transfer
Numerical Analysis of Mixed Convection in Vented Curved Cavity With a Metal Foam Layer
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ABSTRACT<p>Heat transfer applications usually contemplated day‐to‐day are primarily spotlighted on mixed convection, such as solar collector heating arrangements, electronic cooling, and drying processes. Enhancing convection heat transmission in such appliances can be achieved by inserting porous media, inflow loci, and/or line geometry. In the present paper, convection heat transmission inside a vented curved cavity () with an inserted metal foam layer ( PPI and 0.9% porosity) saturated with water was accomplished. The bottom cavity wall was discretely heated at a constant hot temperature, and the curved wall was kept at a constant cold temperature. Governing equations comprising cont</p> ... Show More
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Publication Date
Sun Nov 01 2020
Journal Name
Journal Of Physics: Conference Series
Synthesis, Characterization and Biological Activity of Mixed Ligand Metal Salts Complexes with Various Ligands
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Metal (III) and (II) coordination compounds of o- phenylenediamine, oxalic acid dihydrate and 8-hydroxyquinoline were synthesized for mixed ligand complexes and characterized using FT-IR, UV-Vis and mass spectra, atomic absorption, elemental analysis, electric conductance and magnetic susceptibility measurements. In addition, thermal behavior (TGA) of the metal complexes (1-6) showed good agreement with the formula suggested from the analytical data. The stoichiometric reaction between the metal (III) and (II) ions with three various ligands in molar ratio at aqueous ethyl alchol for (1:1:1:1) (M: O-PDA: OA: 8-HQ) [where M = Cr+3, Mn+2, Co+2, Ni+2. Cu+2 and Zn+2; O-PDA = O-Phenylenediamine; OA = Oxalic acid and 8-HQ = 8-Hydroxyquinoline]. R

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Publication Date
Sun Nov 01 2020
Journal Name
Journal Of Physics: Conference Series
Synthesis, Characterization and Biological Activity of Mixed Ligand Metal Salts Complexes with Various Ligands
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Metal (III) and (II) coordination compounds of o- phenylenediamine, oxalic acid dihydrate and 8-hydroxyquinoline were synthesized for mixed ligand complexes and characterized using FT-IR, UV-Vis and mass spectra, atomic absorption, elemental analysis, electric conductance and magnetic susceptibility measurements. In addition, thermal behavior (TGA) of the metal complexes (1-6) showed good agreement with the formula suggested from the analytical data. The stoichiometric reaction between the metal (III) and (II) ions with three various ligands in molar ratio at aqueous ethyl alchol for (1:1:1:1) (M: O-PDA: OA: 8-HQ) [where M = Cr+3, Mn+2, Co+2, Ni+2. Cu+2 and Zn+2; O-PDA = O-Phenylenediamine; OA = Oxalic acid and 8-HQ = 8-Hydroxyquinoline]. R

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Publication Date
Sun Nov 01 2020
Journal Name
Journal Of Physics: Conference Series
Synthesis, Characterization and Biological Activity of Mixed Ligand Metal Salts Complexes with Various Ligands
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Abstract<p>Metal (III) and (II) coordination compounds of o- phenylenediamine, oxalic acid dihydrate and 8-hydroxyquinoline were synthesized for mixed ligand complexes and characterized using FT-IR, UV-Vis and mass spectra, atomic absorption, elemental analysis, electric conductance and magnetic susceptibility measurements. In addition, thermal behavior (TGA) of the metal complexes (1-6) showed good agreement with the formula suggested from the analytical data. The stoichiometric reaction between the metal (III) and (II) ions with three various ligands in molar ratio at aqueous ethyl alchol for (1:1:1:1) (M: O-PDA: OA: 8-HQ) [where M = Cr+3, Mn+2, Co+2, Ni+2. Cu+2 and Zn+2; O-PDA = O-Phenylenediamine; OA = Oxal</p> ... Show More
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Publication Date
Fri Feb 01 2019
Journal Name
Journal Of Economics And Administrative Sciences
Comparison of classical method and optimization methods for estimating parameters in nonlinear ordinary differential equation
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 ABSTRICT:

  This study is concerned with the estimation of constant  and time-varying parameters in non-linear ordinary differential equations, which do not have analytical solutions. The estimation is done in a multi-stage method where constant and time-varying parameters are estimated in a straight sequential way from several stages. In the first stage, the model of the differential equations is converted to a regression model that includes the state variables with their derivatives and then the estimation of the state variables and their derivatives in a penalized splines method and compensating the estimations in the regression model. In the second stage, the pseudo- least squares method was used to es

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Publication Date
Sun Mar 17 2019
Journal Name
Baghdad Science Journal
Faber Polynomial Coefficient Estimates for Subclass of Analytic Bi-Bazilevic Functions Defined by Differential Operator
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In this work,  an explicit formula for a class of Bi-Bazilevic univalent functions involving differential operator is given, as well as the determination of upper bounds for the general Taylor-Maclaurin coefficient of a functions belong to this class, are established Faber polynomials are used as a coordinated system to study the geometry of the manifold of coefficients for these functions. Also determining bounds for the first two coefficients of such functions.

         In certain cases, our initial estimates improve some of the coefficient bounds and link them to earlier thoughtful results that are published earlier.

 

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