كلية العلوم الرياضية والاحصاء
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Item The Telegraph Equation by Double Laplace Transform And Adomian Decomposition Methods(Al-Neelain University, 2022-03) Nosiba Mohammed Alsadig MohammedAbstract In this paper, we talked about some basic concepts in fractional calculus, and we talked about the Laplace transform of fractional calculus and double Laplace transform of fractional. We also applied the fractional double Laplace and double Laplace adomian decomposition method to solve the fractional telegraph equation. الخلاصة في هذا البحث اسسنا بعض المفاهيم الاساسية في الحسبان الكسري، وحددنا تحويل لابلاس الكسري والتحويل الثنائي للابلاس الكسري. كما قمنا بتطبيق التحويل الثنائي للابلاس الكسري والتحويل الثنائي للابلاس أدوميان الكسري في حل معادلة التلغراف الكسرية.Item Comparison Between Modified and Laplace Homotopy Perturbation Method for Heat Equation and Burger Equation(Al-Neelain University, 2022-03) ANFAL ATTALLAH SALIM HAMDANAbstract In this research, we deal with fractional calculus and use the Adomian Decomposition method, Homotopy perturbation method, modified Homotopy perturbation method and Laplace Homotopy Perturbation method. to find approximate solutions of linear and nonlinear partial differential equations such as the Heat equation and Burger equation. المستخلص تناولنا في هذا البحث الحسبان الكسري و استخدمنا طريقه تفكيك أدوميان وطريقه اضطراب الهوموتبي وطريقه اضطراب الهوموتبي المعدلة وطريقه اضطراب الهوموتبي لابلاس لإيجاد حلول تقريبية للمعادلات التفاضلية الجزئية الخطية وغير الخطية كمعادلة الحرارة ومعادلة بيرجر.Item Unsteady flow of a second grade fluid over an unsteady stretching sheet(Al-Neelain University, 2022-01) Ghada Ali Awad MohamedAbstract In this study we investigate the flow of a second grade fluid numerically. The system of nonlinear partial differential equations governed the flow reduces into one partial differential equation by using the boundary layer approximation and moreover we transform this equation from partial to the ordinary form by means of a suitable similarity transformation. Subject to proper boundary conditions the spectral local linearization method has been used to get the approximate solution. Our results were presented in the form of tables and graphs to show the effects of physical governing parameters. الخلاصة في هذه الدراسة تحققنا عددياً من تدفق مائع من الدرجة الثانية, المعادلات الحاكمة لهذا النموذج هي معادلات تفاضلية جزئية غير خطية تم تقليصها لمعادلة تفاضلية جزئية واحدة باستخدام تقريب الطبقة الحدية , ومن ثم قمنا بتحويل هذه المعادلة لمعادلة تفاضلية عادية باستخدام التحويلات المتشابهه محكومة بشروط حدية مناسبة وتم حلها عددياً باستخدام طريقة الطيف محلية الخطيه , ومن ثم تم عرض النتائج في شكِل جداول ورسومات لنرى الأثر الفيزيائى للعوامل المؤثرة .Item Mathematical Model of Corona Virus Disease (COVID-19): A case Study of Saudi Arabia(Al-Neelain University, 2022-01) Ahmed Elfatih Bedreldeen Abulgasimمستخلص يُعد مرض فيروس كورونا (كوفيد -91) من أكثر الأمراض انتشارًا حول العالم ، حيث أصاب جميع الدول الفقيرة والمتقدمة في العالم بسبب انتشاره بين كبار السن خاصة المصابين بأمراض قوية. قدمنا في هذه الرسالة نموذجاً رياضياً لدراسة انتشار فيروس كورونا في المملكة العربية السعودية بمقاييس مختلفة ودرسنا تأثيرات الأفراد خلال فترة انتشار المرض. وأظهرت نتائج الدراسة أنه عند تعرض الفرد لفيروس كورونا ، توقع النموذج حالات جديدة. وفقًا للنتائج ، من المتوقع أن تحدث ذروة الوباء مع حوالي 335 ألف حالة إخبارية يوميًا. أظهرت النتائج أن العدد الأساسي للتكاثر يتناقص مع وجود قيود معينة له دور حيوي في منع انتشار هذا الوباء في هذا الوضع الحالي Abstract The Corona virus disease (Covid-19) is one of the most prevalent diseases around the world which a ected all the poor and developed countries of the world due to its spread among the elderly especially those with strong diseases. In this thesis we presented a mathematical model to study the spread of Corona virus in the Saudi Arabia under di erent measures and we studied the e ects of individuals during the disease period of the spread of the disease. The results of the study showed that when the individual is exposed to Corona virus .The model forecasted new cases. According to the results, the pandemic peak is expected to take place with about 335 thousands news cases per day. The results show that basic reproductive number is decrease with certain restriction has a vital role in preventing theItem Numerical Solution for Unsteady Oldroyd – B Nanofluid Flow Over Stretching Surface Using the (SLLM)(Al-Neelain University, 2020-12) Mohamed Salah Mohamed Alhajخــلاصــة مسألة أولدرويد ــ بـي لسريان مائع نانوي غير مستقر على سطح متــمدد درست عددياً بإستخدام طريقة الطيف محلية الخطية. حيث ان المــعادلات التفاضلية العاديــة عالية اللاخطية التى تحكــم حركة المائع حولــت الى نظام معادلات تفاضلية عاديـة في صيغتها شبيـــهة الخطية والمشتقة عنــد كــل نقــطة قــدرت بواسطة نقاط تشيبشيف. من خلال الحــل عرضنــا تأثـير الوسائط اللابعدية على الكميات السرعة، الحرارة، الجزيئات النانوية، إعاقة السطح، معدل إنتقال الحرارة عبـر السطح و معدل إنتقال الجزيئات النانويــة عبر السطـح و النتائــج التى تم التوصل لها عرضت فــي شــكل جــداول ورســومـات. يمــكننا أن نقول أن للوسائـط اللابـعدية تأثير على سرعــة سريــان المائع كمــا أن لها تأثير على إنتقال الحـرارة و الجزيئــات النانوية عبـر الســطح. Abstract The problem of the unsteady Oldroyd-B nanofluid flow over stretching surface has been investigated numerically using the Spectral Local Linearization Method (SLLM). The highly nonlinear governing ordinary differential equations representing the motion of nanofluid flow has been transformed into a system of semi-linear ordinary differential equations using the local linearization method. Furthermore, we evaluated the derivative at each point with the Chebyshev collocation points. Through the solution we presented effects of dimensionless parameters on quantities velocity, temperature, nanoparticle volume fraction, skin friction, Nusselt number, and Sherwood number. The obtained results have been presented in tabular and graphical forms. We found that the dimensionless parameters have effects on nanofluid flow velocity, and on heat and nanoparticle transfer on the surface.Item Mathematics '(Alneelain University, 2014) Mohammed Hassen ElzubairAbstract In this research we utilized twister theory to describe the geometry of space-time. The twistors are derived from Spinors which are also used to write zero rest- mass fields equations. We mainly used the properties of twistor filnction to generate zero rest- mass fields, where this function is formulated from both the geometry and topology of Minkowski spaceItem Some Harvesting Problems(Alneelain University, 2015-07) Ranya Hamid El NourABSTRACT. The aim of this thesis is to study and solve optimal control problems for systems driven by both: Brownian motion and Levy processes. The methods of solution used are: Dynamic programming, and Maximum principle where the known Clark-Ocone theorem is applied. The application of Clark-Ocone theorem needs the existence of Malliavin derivative and its extesion in L2 spaces. As an application , the thesis considered an example of harvesting problem in a crowded media as well as searching for optimal portfolio strategies in hedging options in markets driven by both: Brovmian motion and Levy processes.Item Analysis of a Mathematical Model of Malaria Disease(2018-01) Mohamed Kamalaldin Mohamed BabekirAbstract Malaria is one of the deadliest diseases around the world causing the death of around 429,000 person in the year 2015 only. This led the scientists around the world to work hard to fight against the disease. In this study, we analyzed the mathematical model of malaria transmission. We calculated R0 which could determine the future of the disease. We examined two sets of parameters, low prevalence and high prevalence and we calculated the effect rate of all parameters using sensitive analysis. Numerical simulations are carried out to confirm the analytical results and explore the possible behavior of the formulated model.Item Mathematical Analysis of a Compartmental Model for Malaria(2018-01) Shahenaz Osman Khalifa MohammedAbstract In this thesis a mathematical model of malaria transmission has been studied, in which we not only considered the recovered humans return to the susceptible class, but also considered the recovered humans return to the infectious class. We explained some historical and biological concepts of the disease. Also we presented conditions for positivity and boundedness of solution. The existence of the disease-free equilibrium and endemic equilibrium points has been proved. The stability of equilibrium points are determined by next generation matrix method. The analytical results are explained numerically. From these results it is found that if we want control and eradicate the malaria, it is very necessary to decrease the relapse rate and increase the recovery rate.Item Mathematical Model for Cholera Epidemic with Quarantined Sub-Infected Population(2017) Ahmed Adam Younis AhmedAbstract Cholera is an epidemic disease caused by the bacteria Vibrio cholera. In this thesis, nonlinear mathematical models for spread of an infectious epidemic cholera disease with carriers in environment and transmission dynamics are developed and analysed. It is assumed that all susceptible are a ected by carrier population density. These models illustrate how population interact with each other depending on certain rates. By varying some parameters the models can be studied. This thesis analyzes the mathematical models created and shows the implementation of the numerical method Runge-Kutta of order four. The numerical simulations show that for certain parameter values