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Register a new userThe Numerical Solution of Linear Fifth-Order Boundary-Value Problems by Using Spline functions
الحل العددي لمسائل القيم الحدية الخطية من المرتبة الخامسة باستخدام دوال شرائحية
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سليمان محمود( باحث )
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يقدم هذا العمل الحل العددي لمسألة القيم الحدية الخطية المعممة من المرتبة الخامسة. تم فيه تحويل مسألة القيم الحدية المذكورة إلى ثلاث مسائل قيم ابتدائية ثم تطبيق الدوال الشرائحية مع أربع نقاط مجمعة إلى مسائل القيم الابتدائية. إن الطريقة الشرائحية المقترحة تمكننا من إيجاد الحل الشرائحي التقريبي لمسألة القيم الحدية و مشتقاته حتى المرتبة الخامسة. و قد تم اختبار فعالية الطريقة المقترحة باستخدامها لحل أربع مسائل، حيث كانت النتائج التي تم التوصل إليها دقيقة بالمقارنة مع طرائق أخرى.
In this paper, the numerical solution of general linear fifth-order boundary-value problem (BVP) is considered. This problem is transformed into three initial value problems (IVPs) and then spline functions with four collocation points are applied to the three IVPs. The presented spline method enables us to find the spline solution and derivatives up to fifth-order of BVP. By giving four examples and comparing with the other methods, the efficiency and highly accurate of the method will be shown.
References used
DAVIES A. R., A. KARAGEORGHIS, T. N. PHILLIPS, Spectral galerkin methods for primary two-point boundary-value problem in modelling viscoelastic flows, Int. J. Num. Methods Eng. 26 (1988) 647-662
KARAGEORGHIS A., T.N. PHILLIPS, A. R. DAVIES, Spectral collocation methods for the primary two-point boundary-value problem in modeling viscoelastic flows, Int. J. Num. Methods Eng. 26 (1988) 805-813
KHAN M. A., SIRAJ-ul-Islam, TIRMIZI I. A., TWIZELL E. H. ASHRAF S., A Class of methods based on non-polynomial sextic Spline functions for the solution of a special fifth-order boundary-value problems, J. Math. Anal. Appl. 321 (2006) 651- 660
LAMNII A., MRAOUI H., SBIBIH D., TIJINI A., Sextic Spline solution of fifthorder boundary value problems, Math. Comput. Simul. 77 (2008) 237-246
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