The operational matrices for Elliptic Partial Differential
Equations with mixed boundary conditions

Myasar Obaid Enadi; Majeed A. Al-Jawary

doi:10.1088/1742-6596/2857/1/012027

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Publication Date

Tue Oct 01 2024

Journal Name

Journal Of Physics: Conference Series

Volume

2857

DOI

10.1088/1742-6596/2857/1/012027

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The operational matrices for Elliptic Partial Differential Equations with mixed boundary conditions

Myasar Obaid Enadi

Majeed A. Al-Jawary

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AbstractThe 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>xi </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∞ </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.

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Publication Date

Sun Jan 01 2012

Journal Name

Evidence-based Complementary And Alternative Medicine

Gelam Honey Inhibits the Production of Proinflammatory, Mediators NO,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mtext>PGE</mml:mtext></mml:mrow><mml:mtext>2</mml:mtext></mml:msub></mml:mrow></mml:math>, TNF-α, and IL-6 in Carrageenan-Induced Acute Paw Edema in Rats

Saba Zuhair

Kamaruddin

Suzana

Yasmin Anum

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Natural honey is well known for its therapeutic value and has been used in traditional medicine of different cultures throughout the world. The aim of this study was to investigate the anti-inflammatory effect of Malaysian Gelam honey in inflammation-induced rats. Paw edema was induced by a subplantar injection of 1% carrageenan into the rat right hind paw. Rats were treated with the nonsteroidal anti-inflammatory drug (NSAID) Indomethacin (10 mg/kg, p.o.) or Gelam honey at different doses (1 or 2 g/kg, p.o.). The increase in footpad thickness was considered to be edema, which was measured using a dial caliper. Plasma and paw tissue were collected to analyze the production of inflammatory mediators, such as NO, PGE₂

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Publication Date

Tue Dec 01 2020

Journal Name

Results In Physics

Alpha clustering preformation probability in even-even and odd-A<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e3355" altimg="si39.svg"><mml:msup><mml:mrow /><mml:mrow><mml:mn>270</mml:mn><mml:mo>−</mml:mo><mml:mn>317</mml:mn></mml:mrow></mml:msup></mml:math>(116 and 117) using cluster formation model and the mass formulae : KTUY05 and WS4

Norah A.M.

Saad M.

H.

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