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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
Tue Dec 23 2025
Journal Name
Technical University Of Munich
Conditions for Applying Public Private Partnership PPP in Iraq Infrastructure Projects Successfully
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Public private partnership PPP is a method to procure public projects in order to achieve additional value for money in terms of efficiency and quality of services. This thesis studies the concepts of PPP, advantages and disadvantages of PPP. In addition, current Iraq infrastructure projects situations and needs, as well as, some aspects relating to the Iraq’s construction market, legal and contract systems were discussed. A financial model was carried out and applied to a real-life case study project. Finally, a survey targeted researchers; public and private- sectors were applied.

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Publication Date
Sun Jun 07 2015
Journal Name
Baghdad Science Journal
Optimum conditions for Inulinase production by Aspergillus niger using solid state fermentation
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Thirty local fungal isolates according to Aspergillus niger were screened for Inulinase production on synthetic solid medium depending on inulin hydrolysis appear as clear zone around fungal colony. Semi-quantitative screening was performed to select the most efficient isolate for inulinase production. the most efficient isolate was AN20. The optimum condition for enzyme production from A. niger isolate was determined by busing a medium composed of sugar cane moisten with corn steep liquor 5;5 (v/w) at initial pH 5.0 for 96 hours at 30 0C . Enzyme productivity was tested for each of the yeast Kluyveromyces marxianus, the fungus A. niger AN20 and for a mixed culture of A. niger and K. marxianus. The productivity of A. niger gave the highest

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Publication Date
Sun Sep 01 2019
Journal Name
Journal Of Physics: Conference Series
Recovery of temporal coefficient for heat equation from non-local overdetermination conditions
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Abstract<p>Recovery of time-dependent thermal conductivity has been numerically investigated. The problem of identification in one-dimensional heat equation from Cauchy boundary data and mass/energy specification has been considered. The inverse problem recasted as a nonlinear optimization problem. The regularized least-squares functional is minimised through lsqnonlin routine from MATLAB to retrieve the unknown coefficient. We investigate the stability and accuracy for numerical solution for two examples with various noise level and regularization parameter.</p>
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Publication Date
Tue Dec 01 2020
Journal Name
Baghdad Science Journal
The Numerical Technique Based on Shifted Jacobi-Gauss-Lobatto Polynomials for Solving Two Dimensional Multi-Space Fractional Bioheat Equations
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This article deals with the approximate algorithm for two dimensional multi-space fractional bioheat equations (M-SFBHE). The application of the collection method will be expanding for presenting a numerical technique for solving M-SFBHE based on “shifted Jacobi-Gauss-Labatto polynomials” (SJ-GL-Ps) in the matrix form. The Caputo formula has been utilized to approximate the fractional derivative and to demonstrate its usefulness and accuracy, the proposed methodology was applied in two examples. The numerical results revealed that the used approach is very effective and gives high accuracy and good convergence.

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Publication Date
Sun Jul 01 2018
Journal Name
Computers &amp; Mathematics With Applications
Analytical and numerical solutions for the nonlinear Burgers and advection–diffusion equations by using a semi-analytical iterative method
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Publication Date
Fri Jan 01 2016
Journal Name
Journal Of Engineering
Enhanced Chain-Cluster Based Mixed Routing Algorithm for Wireless Sensor Networks
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Energy efficiency is a significant aspect in designing robust routing protocols for wireless sensor networks (WSNs). A reliable routing protocol has to be energy efficient and adaptive to the network size. To achieve high energy conservation and data aggregation, there are two major techniques, clusters and chains. In clustering technique, sensor networks are often divided into non-overlapping subsets called clusters. In chain technique, sensor nodes will be connected with the closest two neighbors, starting with the farthest node from the base station till the closest node to the base station. Each technique has its own advantages and disadvantages which motivate some researchers to come up with a hybrid routing algorit

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Publication Date
Tue Sep 01 2020
Journal Name
Journal Of Engineering
Performance Evaluation of Scalar Multiplication in Elliptic Curve Cryptography Implementation using Different Multipliers Over Binary Field GF (2233)
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This paper presents a point multiplication processor over the binary field GF (2233) with internal registers integrated within the point-addition architecture to enhance the Performance Index (PI) of scalar multiplication. The proposed design uses one of two types of finite field multipliers, either the Montgomery multiplier or the interleaved multiplier supported by the additional layer of internal registers. Lopez Dahab coordinates are used for the computation of point multiplication on Koblitz Curve (K-233bit). In contrast, the metric used for comparison of the implementations of the design on different types of FPGA platforms is the Performance Index.

The first approach attains a performance index

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Publication Date
Wed May 10 2023
Journal Name
Journal Of Engineering
Damage Detection and Assessment of Stiffness and Mass Matrices in Curved Simply Supported Beam Using Genetic Algorithm
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In this study, a genetic algorithm (GA) is used to detect damage in curved beam model, stiffness as well as mass matrices of the curved beam elements is formulated using Hamilton's principle. Each node of the curved beam element possesses seven degrees of freedom including the warping degree of freedom. The curved beam element had been derived based on the Kang and Yoo’s thin-walled curved beam theory. The identification of damage is formulated as an optimization problem, binary and continuous genetic algorithms
(BGA, CGA) are used to detect and locate the damage using two objective functions (change in natural frequencies, Modal Assurance Criterion MAC). The results show the objective function based on change in natural frequency i

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Publication Date
Tue Jan 01 2019
Journal Name
Energy Procedia
Improvement the Superconducting properties of TlBa2 Ca2 Cu3xNix O 9-δ superconducting compound by partial substitution of copper with nickel oxide on the
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Publication Date
Tue Jan 01 2019
Journal Name
Aip Conference Proceedings
Studying the partial substitution of barium with cadmium oxide and its effect on the electrical and structural properties of HgBa2Ca2Cu3O8+δ superconducting compound
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