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"المعادلات الجبرية"
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Application of Adomian Decomposition Method for Solving Helmholtz Equation
The Adomian decomposition method (ADM) is effective for solving linear and nonlinear ordinary and partial differential equations, integral equations, algebraic equations and integro differential equations and it leads to an analytical solution in the form of an infinite power series. We will solve the Helmholtz equation in two dimensional by the Adomian decomposition method.
Journal Article
Solving 3D Helmholtz Equation Using Triple Laplace-Aboodh-Sumudu Transform
This paper introduces a novel integral transform, termed the triple Laplace-Aboodh-Sumudu transform (TLAST), by combining the Laplace transform, Aboodh transform, and Sumudu transform. The primary objective of this research is to utilize TLAST for solving the Helmholtz equation in three dimensions. The TLAST provides a powerful tool for transforming complex partial differential equations into algebraic equations, simplifying their solution. The paper presents the mathematical formulation of TLAST and demonstrates its application in solving the Helmholtz equation. By employing TLAST, the solution to the Helmholtz equation is obtained efficiently, highlighting the potential of this new integral transform in addressing various problems in science, engineering, and other fields.
Journal Article
اللمعة الماردينية في شرح الياسمينية
يتناول كتاب (اللمعة الماردينية في شرح الياسمينية) والذي قام بتأليفه ( محمد بن محمد بن بدر الدين سبط المارديني) في حوالي (77) صفحة من القطع المتوسط موضوع (الجبر) مستعرضا المحتويات التالية : ابن الياسمين، حياته .. سيرته، ابن الياسمين العالم الرياضي، وصف موجز للياسمينة ولشرح المارديني عليها، تعريف بالشارح، الأرجوزة الياسمينية، اللمعة الماردينية في شرح الياسمينية، التكملة الأولى، التكملة الثانية، ثم الخاتمة والمصادر والمراجع.
Book
On Triple Laplace-Aboodh-Shehu Transform and its Properties with Applications
In this paper, we combine the Laplace transform, Aboodh transform and Shehu transform to give another transform which is called the triple Laplace-Aboodh-Shehu transform. This interesting transform reduce a linear partial equation of second order with unknown function of three variables to an algebraic equation, which can then be solved by applying the inverse triple Laplace-Aboodh-Shehu transform.
Journal Article