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Register a new userNumerical Method for Finding Single and Multiple Integrals
طريقة عددية لإيجاد التكاملات الأحادية و الثنائية و الثلاثية
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تم في هذا البحث تقديم طريقة عددية تكرارية لإيجاد القيم التقريبية للتكاملات الأحادية و الثنائية و الثلاثية. تعتمد الطريقة المقترحة على تقريب دالة التكاملات الأحادية بكثيرة حدود شرائحية من الدرجة الخامسة، ثم استخدام نقاط غوص-ليجندر بالإضافة إلى التقريبات الشرائحية لإيجاد التكاملات الثنائية و الثلاثية. تبين الدراسة أن الطريقة تكون متقاربة من الرتبة السادسة عند تطبيقها لإيجاد التكاملات الأحادية، و تكون أيضا متقاربة من الرتبة السادسة عند تطبيقها لإيجاد التكاملات الثنائية و الثلاثية باستخدام ثلاث نقاط غوصية أو أكثر. تم اختبار فعالية الطريقة المقترحة بتطبيقها لإيجاد بعض التكاملات الأحادية و الثنائية و الثلاثية المختلفة ثم مقارنة نتائج هذه الطريقة مع نتائج بعض الطرائق الأخرى.
In this paper, an iterative numerical method for obtaining approximate values of definite single, double and triple integrals will be illustrated. This method depends on approximating the single integral function by spline polynomial of fifth degree, while Gauss Legendre points as well as spline polynomials are used for finding multiple integrals. The study shows that when the method are applied to single integrals is convergent of order sixth, as well as when applied to triple integrals is convergent of order sixth for three Gauss Legendre points or greater. Errors estimates of the proposed method alongside numerical examples are given to test the convergence and accuracy of the method.
References used
HASHISH H., S.H. Behiry, N.A. El-Shamy, Numerical integration using wavelets, Applied Mathematics and Computation 211 (2009) 480-487
(SIRAJ-ul-Islam , Imran Aziz , Fazal Haq, A comparative study of numerical integration based on Haar wavelets and hybrid functions, Computers and Mathematics with Applications, doi:10.1016, pp.1-12, (2010
RATHOD H.T., K.V. Nagaraja, B. Venkatesudu, Numerical integration of some functions over an arbitrary linear tetrahedra in Euclidean three-dimensional space, Applied Mathematics and Computation 191 (2007) 397-409
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