Abstract
A method based on extended cubic B-spline is proposed to solve a linear system of second-order boundary value problems. In this method, two free parameters, lambda _{1} and lambda _{2}, play an important role in producing accurate results. Optimization of these parameters are carried out and the truncation error is calculated. This method is tested on three examples. The examples suggest that this method produces comparable or more accurate results than cubic B-spline and some other methods.
Highlights
It is well-known that many real life phenomena in physics and engineering can be modelled by systems of linear and nonlinear differential equations
One class of these systems is of second order boundary value problems
The existence of solution to such system was studied in Chen et al (2005), Cheng and Zhong (2005), Thompson and Tisdell (2002)
Summary
It is well-known that many real life phenomena in physics and engineering can be modelled by systems of linear and nonlinear differential equations. One class of these systems is of second order boundary value problems. The main purpose of our Heilat et al SpringerPlus (2016) 5:1314 present study is to apply a spline function in solving Eq (1). This equation had already been treated using cubic B-spline, cubic B-spline scaling functions, sinc-collocation, and spline collocation approaches (Caglar and Caglar 2009; Dehghan and Lakestani 2008; ElGamel 2012; Khuri and Sayfy 2009)
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