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Register a new userAlgorithm to solve nonlinear Advection Equation numerically using cubic Bspline
خوارزمية لحل معادلة الحمل غير الخطية بطريقة عددية باستخدام توابع B-spline التكعيبية
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نقدم في هذا البحث حل تقريبياً لمعادلة الحمل باستخدام طريقة العناصر المنتيية. تقوم هذه الطريقة على تحويل معادلة الحمل غير الخطية إلى جملة معادلات تفاضلية عادية بالاستفادة من بعض أشكال توابع B-spline التكعيبية. ثم حل هذه الجملة باستخدام طريقة SSP-RK54 و قد وضعنا خوارزمية مفصلة تبين مراحل العمل بشكل دقيق. و قمنا . بكتابة برنامج لتنفيذ هذه الخوارزمية نفذناه على مجموعة من الأمثلة لها حلول تحليلية معلومة ثم حسبنا الخطأ المرتكب لتقييم جودة الطريقة. و وجدنا أن هذه الطريقة تعطي حلولا تقريبية جيدة لمسألة الحمل.
In this paper, we introduce an algorithm to solve the Advection equation by finite element method. In this method, we have chosen Three pattern of cubic B-Spline to approximate the nonlinear solution to convert the nonlinear PDE into a system of ODE, Then we solved this system equation by SSP-RK54 method, And we made a program implementing this algorithm and we checked the program using some examples, which have exact solutions, then we evaluate our results. As a conclusion we found that this method gives accurate results for advection equation.
References used
ARORA G, SINGH BK,-2013-Numerical solution of Burgers’ equation with modified cubic B-spline differential quadrature method. Appl Math Comput ,224,166–77
BAKODAH HO, 2016-A Comparative Study of Two Spatial Discretization Schemes for Advection equation. International Journal of Modern Nonlinear Theory and Application, 5, 59-66
BELLMAN R, KASHEF BG, CASTI J,1972- Differential quadrature: a technique for the rapid solution of nonlinear differential equations. J Comput Phy, 10,40–52
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