طرائق شرائحية من الدرجة السابعة في الفضاء C3 مع أربع نقاط مجمعة لحل مسائل القيم الحدية الخطية من المرتبة الثالثة
Abstract
تم في هذا البحث استخدام كثيرات حدود شرائحية من الدرجة السابعة في الفضاء C3 لصياغة طرائق عددية لحل مسائل القيم الحدية في المعادلات التفاضلية الخطية من المرتبة الثالثة [1,2,3,4]، وأيضا لحل مسألة القيمة الحدية المتعددة الحالات من المرتبة الثالثة [5,6,7,8,9,10]. تعتمد الطرائق على أربع نقاط مجمعة: ( j=1,2,3,4), في كل مجال جزئي ، حيث ، (i=1,2,...n)، ، ، ، و . تبين الدراسة أن الطرائق المقدمة عندما تطبق لحل مثل هذه المسائل تكون متقاربة ومرتبة التقارب هي السابعة على الأقل مهما تكن و. تشكل الطرائق المدروسة مناطق غير محدودة من الاستقرار المطلق في المستوي العقدي من أجل بعض القيم لـ في المجال .
أجرينا بعض تجارب المحاكاة العددية على بعض المسائل لتوضيح عمل الطريقة المقترحة مقارنة مع طرائق عددية موجودة في دراسات سابقة.
We use C3-seventh polynomial splines to establish numerical methods for solving third-order linear boundary value problems [1,2,3,4] and a system of third-order boundary value problems associated with third-order obstacle problems [5,6,7,8,9,10]. These methods depend on four collocation points , j=1,...,4 in each subinterval , where , i=1(1)n, , , , and . A study shows that the presented methods are convergent and their order of convergence is at least seven for all and . Moreover, analysis of stability appears that the method possesses unbounded regions of absolute stability for some. Numerical experiments and comparisons with other available results are given to illustrate the applicability and efficiency of the presented methods.
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