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Register a new userA Software Solution for Nonlinear Advection Equation based on Finite Differences Methods
حل برمجي لمعادلة الحمل غير الخطية بالاعتماد على طرائق الفروق المنتهية
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يقدم هذا البحث حلول تقريبية لمعادلة الحمل باستخدام الفروق المنتهية. تقوم هذه الحلول على تحويل معادلة الحمل غير الخطية إلى جملة معادلات غير خطية بالاستفادة من بعض طرائق الفروق المنتهية. و حل هذه الجملة باستخدام طريقة نيوتن يعتمد على طريقة غاوس سيدل. و وضعت خوارزمية مفصلة تبين مراحل العمل بشكل دقيق. تم وضع برنامج ينفذ هذه الخوارزمية على مجموعة من الأمثلة لها حلول تحليلية معلومة ثم حسبنا الخطأ المرتكب لتقييم جودة الطريقة. و وجد أن هذه الطريقة تعطي حلولً تقريبية جيدة لمسألة الحمل.
In this paper, we present approximate solutions for the Advection equation by finite differences method. In this method we convert the nonlinear partial differential equation into a system of nonlinear equations by some finite differences methods. Then this system was solved by Newton's 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
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
CAUSON D M, MINGHAM C G,2010- Introductory Finite Difference Methods For PDES. Ventus Publishing
Courant, R., K. O. Fredrichs, and H. Lewy (1928), Uber die Differenzengleichungen der Mathematischen Physik, Math. Ann, vol.100, p.32, 1928
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