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Register a new userApproximate Solutions of Twelfth-Order Boundary Value Problems by Using Spline Technique
حلول تقريبية لمسائل القيم الحدية من المرتبة الثانية عشرة باستخدام تقنية شرائحية
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Tishreen University ورقة بحثية
Publication date
2017
fields
Mathematics
and research's language is
العربية
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تم تقديم طريقة تجميع شرائحية للحل العددي لمسائل القيم الحدية الخطية في المعادلات التفاضلية المعممة من المرتبة الثانية عشرة التي تنشأ تطبيقاتها في الميكانيك و العلوم المختلفة. تعتمد التقنية المقترحة على تقريب دالة الحل بحدوديات شرائحية من الدرجة السادسة عشرة مع خمس نقاط تجميع في كل مجال جزئي من الحل. تستطيع الطريقة تقريب الحل للمسألة و تقريب مشتقاته حتى المرتبة الحادية عشرة. تم إثبات أن الطريقة المقترحة تضمن وجود و وحدانية الحل عندما تُطبَّقْ لحل بعض مسائل الاختبار. كما تم تقدير صيغة للخطأ المقتطع الشامل، حيث تبين الدراسة أن الطريقة تكون متناسقة و متقاربة بخطأ مقتطع شامل من الرتبة السادس عشرة. و لإثبات صحة النتائج النظرية قمنا باختبار الطريقة الشرائحية بحل ثلاث مسائل مختلفة، حيث تشير المقارنات لنتائجنا مع نتائج الآخرين إلى أفضلية الطريقة المقترحة من حيث الدقة و الفعالية.
In this paper, we develop spline collocation technique for the numerical solution of general twelfth-order linear boundary value problems (BVPs). This technique based on polynomial splines from order sixteenth as well as five collocation points at every subinterval of BVPs. The method developed not only approximates the solution of BVP, but its higher order derivatives as well. We show that the spline collocation method is existent and unique when it is applied into a test problem. Also, its global truncation error is estimated. Moreover, the purposed spline method when applied to test problems will be consistent and convergent from sixteenth order. Three numerical examples are given to illustrate the applicability and efficiency of the new method. Comparisons of our results with some other methods show that our method is very effective and successful.
References used
AL-HAYANI W. Adomian Decomposition Method with Green’s Function for Solving Twelfth-Order Boundary Value Problems. Applied Mathematical Sciences, Vol. 9, No. 8, 2015, 353-368
ALI J., S. ISLAM, M. T. RAHIM and G. ZAMAN, The Solution of Special Twelfth Order Boundary Value Problems by the Optimal Homotopy Asymptotic Method. World Applied Sciences Journal, Vol.11, No.3, 2010, 371-378
DOHA E. H., W. M. ABD-ELHAMEED, BASSUONY M. A. On the Coefficients of Differentiated Expansions and Derivatives of Chebyshev Polynomials of the Third and Fourth Kinds. Acta Mathematica Scientia, Vol. 35B, No.2, 2015, 326–338
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This research studies the distributive solutions for some partial
differential equations of second order.
We study specially the distributive solutions for Laplas equation,
Heat equation, wave equations and schrodinger equation.
We introduce the
fundamental solutions for precedent equations
and inference the distributive solutions by using the convolution of
distributions concept. For that we use some of lemmas and theorems
with proofs, specially for Laplas equation. And precedent some of
concepts, defintions and remarks.
المعادلة التفاضلية الجزئية من المرتبة الثانية
التوزيعات
الجداء التنسوري للتوزبعات
التفاف التوزيعات
الحلول الأساسية
الحلول التوزيعية
partial differential equations of second order
Distributions
Tensor product of distributions
Convolution of distributions
Fundamental solution
Distributive solution
المزيد..
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