New Spline Method for Solving Linear Two-Point Boundary Value Problems

Abstract

In this research, second order linear two-point boundary value problems are treated using new method based on hybrid cubic B-spline. The values of the free parameter,Gamma , are chosen via optimization. The value of the free parameter plays an important role in giving accurate results. Optimization of this parameter is carried out. This method is tested on four examples and a comparison with cubic B-spline, trigonometric cubic B-spline and extended cubic B-spline methods has been carried out. The examples suggest that this method produces more accurate results than the other three methods. The numerical results are presented to illustrate the efficiency of our method.

Hybrid Cubic B-spline Method for Solving A Class of Singular Boundary Value Problems

“…Consider a partition π of [a, b] is equally-spaced knots x i into n segments [x i , x i+1 ], i = 0, 1, ..., n, where a = x 0 < x 1 < ... < x n = b, such that h = b−a n , x 0 = a, x i = x 0 + ih. Then, the hybrid cubic B-spline functions can be defined as the following relation [17]:…”

“…In this paper, we study a hybrid cubic B-spline method (HCBSM) for solving secondorder singular boundary value problems. The approach used is basically that of [17]. The present method is examined by taking several problems to prove its accuracy.…”

Comprehensive Review of Interpolation Techniques Using B-Spline

“…In (Mat Zin, 2016), the concept introduced in (Akram et al, 2022) was reiterated, demonstrating that outperformed other B-spline techniques in terms of efficiency. The writer's experimentation on non-linear partial differential equations provided more evidence of the effectiveness (Heilat et al, 2021). B-spline interpolating, renowned for its resilience and adaptability, is widely employed in various domains including computer-assisted geometrical design, computation of images, information appropriate, and medical imaging.…”

Cubic Trigonometric B-spline Method for Solving a Linear System of Second Order Boundary Value Problems

“…The aim of this research is to use CTBSM for solving linear system of second order BVPs. The system had already been treated using spline collocation approach [17], cubic B-spline scaling functions [18], B-spline method [19], Extended cubic B-spline method [20], Hybrid cubic B-spline method [21]. CTBSM was developed to solve dynamical systems in [22], the results are promising.…”