پديد آورنده :
فيض اللهي، الهام
عنوان :
حل عددي معادله هاي تحولي غير خطي بر اساس طرح هاي نيمه - لاگرانژي
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
رياضي كاربردي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
نه،95ص.: جدول
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
رضا مختاري
استاد مشاور :
مهدي تاتاري
توصيفگر ها :
معادله تغيير يافته , معادله برگرز
تاريخ نمايه سازي :
11/8/92
استاد داور :
داود ميرزايي، حميدرضا مرزبان
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
Abstract The goal of this study is to extend the modified equation technique to the Burgers equation The modified equation is a technique for evaluating various qualities or properties of a finite difference analogue of a given partial differential equation These qualities include order of accuracy consistency stability dissipation and dispersion Our approach is based on the semi Lagrangian formulation The essential idea of the semi Lagrangian formulation is to combine the Eulerian derivative and the convective term into a Lagrangian derivative Another goal of this study is to attempt to develop highly accurate and efficient semi Lagrangian finite difference methods A new designing algorithm with the aid of the modified equation theory and a new class of numerical methods based on the semi Lagrangian discretization and the modified equation theory for computing solutions to the considerid equations have been introduced The accuracy of the proposed semi Lagrangian finite difference methods are surveyed through careful error analysis We show that the overall accuracy of the proposed semi Lagrangian schemes depends on two factors one is the global truncation error which can be obtained by the modified equation analysis and the other is a generic feature of semi Lagrangian methods which characterize their non monotonic dependence on the time step size In this thesis we inrestigate the semi Lagrangian methods and modified equation technique for solving evolutionary partial differential equations First of all we provide a collection of the required prerequisites including the process of obtaining modified equation Bspline interpolation and also a brief description of the characteristics and the locan one dimensional LOD method to better understand the thesis implications We also verify the high accuracy and unconditional stability of the five point implicit scheme by conducting numerical simulation to the nonlinear Burgers equation which is a canonical nonlinear model to test numerical methods Then the semi Lagrangian formulation of this equation is discretized along the characteristic curve and we have used the second order Runge Kutta method to locate the departure points The solution values at the departure points are obtained by interpolation Therefore we have the interpolative error to obtain the global truncation error of the difference scheme using the modified equation technique An error analysis is conducted for the proposed difference schemes followed by numerical experiments for verification of the analytical results The results of this study suggests a direction where more accurate and efficient semi Lagrangian methods can be developed and where the classical modified equation technique can be easily extended to nonlinear applications In the following we have implemented semi Lagrangian and modified equation PDF created with pdfFactory trial version www pdffactory com
استاد راهنما :
رضا مختاري
استاد مشاور :
مهدي تاتاري
استاد داور :
داود ميرزايي، حميدرضا مرزبان
