Three Point Spline Collocation Method for Solving General Linear and Nonlinear Eighth-Order Boundary-Value Problems

Authors

  • Suliman M Mahmoud

Abstract

In this paper, a spline collocation method is developed for finding numerical solutions of general linear eighth-order boundary-value problems (BVPs) and nonlinear eighth-order initial value problems (IVPs). The presented collocation method affords the spline solution by the polynomial of degree eleventh which satisfies the BVPs and IVPs at three collocation points. The study shows that the spline collocation method when is applied such this problems is existent and unique. Moreover, the purposed method if applied to these systems will be consistent and the global truncation error equal eleventh.

Numerical results are given for four examples to illustrate the implementation and efficiency of the method.  Comparisons of the results obtained by the present method with results obtained by the other methods reveal that the present method is very effective and convenient.

يتم في هذا البحث تطوير طريقة شرائحية لإيجاد الحل العددي لمسائل القيم الحدية الخطية وغير الخطية في المعادلات التفاضلية المعممة من المرتبة الثامنة. الطريقة المقترحة تقدم الحل الشرائحي التقريبي باستخدام كثيرة حدود من الدرجة إحدى عشرة وتلك الحدودية تحقق المسائل الحدية والابتدائية المطروحة في ثلاث نقاط تجميع.

تبين الدراسة أن الطريقة المقترحة عندما تطبق لحل هذه المسائل تكون موجودة ومعرفة بشكل وحيد. كما تظهر الدراسة التحليلية أن الطريقة تكون متجانسة ومتقاربة وأن الخطأ المقتطع الشامل من الرتبة إحدى عشرة. تم اختبار الطريقة الشرائحية بحل أربع مسائل مختلفة، حيث تشير المقارنات لنتائج طريقتنا مع نتائج الطرائق الأخرى إلى أفضلية الطريقة المقترحة من حيث الدقة والفعالية.

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Published

2014-11-17

How to Cite

1.
Mahmoud SM. Three Point Spline Collocation Method for Solving General Linear and Nonlinear Eighth-Order Boundary-Value Problems. TUJ-BA [Internet]. 2014Nov.17 [cited 2025Jul.12];36(6). Available from: http://www.journal.tishreen.edu.sy/index.php/bassnc/article/view/1198

Issue

Vol. 36 No. 6 (2014): العلوم الأساسية

Section

Articles

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