كلية العلوم الرياضية والاحصاء
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Item Applications of the Homotopy Perturbation Method and Sumudu Transform of the Linear and Nonlinear Differential Equations(2018) Sana Hassan Magboul AhmedAbstract This study is mainly focusing on the application of the homotopy perturbation method and Sumudu transform of the linear and nonlinear differential equations. It has established some defnitions and properties of homotopy perturbation method and Sumudu transform. The study combines the homotopy perturbation method and Sumudu transform. Consequently, it gives the solution in series form and approximates components, and _nds the exact solution. Then, it is applied to solve linear and nonlinear differential equations . Finally, the solutions of linear and nonlinear differential equations by this method, and the other methods will be compared. الخلاصة تتمركز هذه الدراسة مجملا في تطبيق طريقة ارتجاج الهموتوبيا وتحويل سمودو في حل المعادلات التفاضلية الخطية وغير الخطية . ستقوم الدراسة بتاسيس بعض التعريفات والخصائص بالنسبة لطريقة الارتجاج الهموتوبيا وتحويل سمودو.قامت الدراسة بدمج طريقة الارتجاج الهموتوبيا وتحويل سمودو. مما ادى الي ايجاد الحل فى شكل متسلسلة وتقريب المكونات لايجاد الحل التام. من ثم طبقت الدراسة لحل المعادلات التفاضلية الخطية وغير الخطية. واخيرا تمت مقارنة حلول المعادلات التفاضلية الخطية وغير الخطية بطرق اخرى.Item Application of the Spectral Local Linearization Method on a System of Nonlinear Ordinary Di erential Equations(Alneelain University, 2016-12) Abubakr Eltayeb Mohammed EltayebIn this study the problem of unsteady nano uid ow over a stretching sheet subject to couple stress e ects is presented. Instead of assuming that the nano-particle volume fraction at the boundary surface may be actively controlled, a realistic boundary condition for the nanoparticle volume fraction model is that the nano-particle ux at the boundary be set to zero. We assume there is no active control of the nano-particle volume fraction at boundary. The spectral local linearisation method has been used to solve the governing equations, moreover the results were further con rmed by using the quasi-linearization method. The qualitative and quantitative e ects of the dimensionless parameters in the problem such as the couple stress parameter, the Prandtl number, the Brownian motion parameter, the thermophoresis parameter and the Lewis number on the uid behavior are determined. i