Matematik ve Bilgisayar Bölümü / Department of Mathematics and Computer Science

Permanent URI for this collectionhttps://hdl.handle.net/11413/6787

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B-spline Interpolation Compared with Finite Difference, Finite Element and Finite Volume Methods Which Applied to Two-Point Boundary Value Problems
(ELSEVIER SCIENCE INC, 360 PARK AVE SOUTH, NEW YORK, NY 10010-1710 USA, 2006-04-01) Çağlar, Hikmet; Çağlar, Nazan; Elfaituri, Khaled; TR114368; TR110809
This paper considers the B-spline interpolation and compares this method with finite difference, finite element and finite volume methods which applied to the two-point boundary value problem. -d/dx(p(x)du/dx) = f(x), a < x < b, u(a) = u(b) = 0.
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B-spline solution of singular boundary value problems
(ELSEVIER SCIENCE INC, 360 PARK AVE SOUTH, NEW YORK, NY 10010-1710 USA, 2006-11-15) Çağlar, Nazan; Çağlar, Hikmet; TR110809; TR114368
Homogeneous and non-homogenous singular boundary value problems (special case) are solved using B-splines. The original differential equation is modified at singular point then the boundary value problem is treated by using B-spline approximation. The method is tested on some model problems from the literature, and the numerical results are compared with exact solution. (c) 2006 Elsevier Inc. All rights reserved.
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Fifth-degree B-spline solution for a fourth-order parabolic partial differential equations
(ELSEVIER SCIENCE INC, 360 PARK AVE SOUTH, NEW YORK, NY 10010-1710 USA, 2008-07-15) Çağlar, Hikmet; Çağlar, Nazan; TR114368; TR110809
In this paper, we find the numerical solution of a fourth-order parabolic partial differential equation. A family of B-spline methods has been considered for the numerical solution of the problems. The results show that the present method is an applicable technique and approximates the exact solution very well. (c) 2008 Elsevier Inc. All rights reserved.
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Solution of fifth order boundary value problems by using local polynomial regression
(ELSEVIER SCIENCE INC, 360 PARK AVE SOUTH, NEW YORK, NY 10010-1710 USA, 2007-03-15) Çağlar, Hikmet; Çağlar, Nazan; TR114368; TR110809
In this paper, we present a novel method based on the local polynomial regression for solving of fifth order boundary value problems. The method is tested on numerical example to demonstrate its usefulness. The method presented in this paper is also compared with those developed by Siddiqi and Akram [Solution of fifth order boundary value problems using nonpolynomial spline technique, Appl. Math. Comput. 175 (2006) 1575-1581], as well and is observed to be better. (c) 2006 Elsevier Inc. All rights reserved.

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